Video Lecture for Electrostatics NEET `PYQ`
NEET 2022
Question 1. Six charges `+q, q, +q, q, +q,` and `q` are fixed at the corners of a hexagon of side d as shown in the figure. The work done in bringing a charge `q_0` to the centre of the hexagon from infinity is ( `\varepsilon_0` - permittivity of free space)
(a) `\frac{-q^2}{4\pi\varepsilon_0 d}(6-\frac{1}{\sqrt{2}})`
(b) Zero
(c) `\frac{-q^2}{4\pi\varepsilon_0 d}`
(d) `\frac{-q^2}{4\pi\varepsilon_0 d}(3-\frac{1}{\sqrt{2}})`
Answer (b)
Question 2. The angle between the electric lines of force and the equipotential surface is
(a) `0^o`
(b) `45^o`
(c) `90^o`
(d) `180^o`
Answer (c)
Question 3. Two hollow conducting spheres of radii `R_1` and `R_2 (R_1 >> R_2)` have equal charges. The potential would be
(a) More on bigger sphere
(b) More on smaller sphere
(c) Equal on both the spheres
(d) Dependent on the material property of the sphere
Answer (b)
Qustion 4. Two point charges `-q` and `+q` are placed at a distance of `L`, as shown in the figure.
The magnitude of electric field intensity at a distance `R(R >> L)` varies as:
(a) `1/R^2`
(b) `1/R^3`
(c) `1/R^4`
(d) `1/R^6`
Answer (b)
NEET 2021
Question 5. Polar molecules are the molecules :
(a) having a permanent electric dipole moment
(b) having zero dipole moment
(c) acquire a dipole moment only in the presence of electric field due to displacement of charges
(d) acquire a dipole moment only when magnetic field is absent
Answer (a)
Question 6. A dipole is placed in an electric field as shown. In which direction will it move?
(a) towards the left as its potential energy will increase.
(b) towards the right as its potential energy will decrease.
(c) towards the left as its potential energy will decrease.
(d) towards the right as its potential energy will increase.
Answer (c)
Question 7. Two charged spherical conductors of radius `R_1` and `R_2` are connected by a wire. Then the ratio of surface charge densities of the spheres `(\sigma_1 /\sigma _2)` is :
(a) `R_1^2/R_2^2`
(b) `R_1/R_2`
(c) `R_2/R_1`
(d) `\sqrt{R_1/R_2}`
Answer (c)
Question 8. Column - I gives certain physical terms associated with flow of current through a metallic conductor. Column-II gives some mathematical relations involving electrical quantities. Match column-I and column-II with appropriate relations.
Column - I Column - II
(A) Drift Velocity (P) `m/{n e^2 p}`
(B) Electrical Resistivity (Q) `n eu_d`
(C) Relaxation Period (R) `{eE}/{m}T`
(D) Current Density (S) `E/J`
(a) (A)-(R); (B)-(Q); (C)-(S); (D)-(P)
(b) (A)-(R); (B)-(S); (C)-(P); (D)-(Q)
(с) (A)-(R); (B)-(S); (C)-(Q); (D)-(P)
(d) (A)-(R); (B)-(P); (C)-(S); (D)-(Q)
Answer (b)
Question 9. Twenty-seven drops of same size are charged at `220V` each. They combine to form a bigger drop. Calculate the potential of the bigger drop.
(a) `1980V`
(b) `660V`
(c) `1320V`
(d) `1520V`
Answer (a)
NEET 2020
Question 10. A short electric dipole has a dipole moment of `16\times10^-9 Cm`. The electric potential due to the dipole at a point at a distance of `0.6 m` from the centre of the dipole, situated on a line making an angle of `60^o` with the dipole axis is :
`(1/{4\pi\varepsilon_0}=9\times10^9 Nm^2/C^2)`
(a) `1980V`
(b) `660V`
(c) `1320V`
(d) `1520V`
Answer (a)
NEET 2020
Question 10. A short electric dipole has a dipole moment of `16\times10^-9 Cm`. The electric potential due to the dipole at a point at a distance of `0.6 m` from the centre of the dipole, situated on a line making an angle of `60^o` with the dipole axis is :
`(1/{4\pi\varepsilon_0}=9\times10^9 Nm^2/C^2)`
(a) `200V`
(b) `400V`
(c) Zero
(d) `50V`
Answer (a)
Question 11. The capacitance of a parallel plate capacitor with air as medium is `6\muF`. With the introduction of a dielectric medium, the capacitance become `30\muF` The permittivity of the medium is :
`(\varepsilon_0 = 8.85\times10^-12 C^2 N^-1 m^-2)`
(a) `1.77\times10^{-12}C^2N^-1m^-2`
(b) `0.44\times10^{-10}C^2N^-1m^-2`
(c) `5.00C^2N^-1m^-2`
(d) `0.44\times10^{-13}C^2N^-1m^-2`
Answer (b)
(b) `0.44\times10^{-10}C^2N^-1m^-2`
(c) `5.00C^2N^-1m^-2`
(d) `0.44\times10^{-13}C^2N^-1m^-2`
Answer (b)
Question 12. In a certain region of space with volume `0.2 m^3`, the electric potential is found to be `5 V` throughout. The magnitude of electric field in this region is :
(a) `0.5N/C`
(b) `1N/C`
(c) `5N/C`
(d) Zero
Answer (d)
Question 13. A spherical conductor of radius 10 cm has a charge of `3.2\times10^-7 C` distributed uniformly. That is the magnetude of electric field at a point `15 cm` from the centre of the sphere? `(1/{4\pi\varepsilon_0}=9\times10^9 Nm^2/C^2)`
(a) `1.28\times10^5 N/C`
(b) `1.28\times10^6 N/C`
(c) `1.28\times10^7 N/C`
(d) `1.28\times10^4 N/C`
Answer (a)
NEET 2019
Question 14. A hollow metal sphere of radius R is uniformly charged. The electric field due to the sphere at a distance r from the centre :
(a) zero as r increases for r < R, decreases as r increases for r > R
(b) zero as r increases for r < R, increases as r increases for r > R.
(c) decreases as r increases for r < R and for r > R.
(d) increases as r increases for r < R and for r > R.
Answer (a)
Question 15. Two point charges A and B, having charges `+Q` and `– Q` respectively, are placed at certain distance apart and force acting between them is F. If `25%` charge of A is transferred to B, then force between the charges becomes :
(a) `F`
(b) `{16F}/9`
(c) `{9F}/16`
(d) `{4F}/3`
Answer (c)
Question 16. A parallel plate capacitor of capacitance `20\muF` is being charged by a voltage source whose potential is changing at the rate of 3V/s. The conduction current through the connecting wires, and the displacement current through the plates of the capacitor, would be, respectively :
(a) zero, zero
(b) zero, `60\muA`
(c) `60\muA`, `60\muA`
(d) `60\muA`, zero
Answer (c)
Question 17. Two parallel infinite line charges with linear charge densities `+\lambdaC/m` and `-\lambdaC/m` are placed at a distance of `2R` in free space. What is the electric field mid-way between the two line charges?
(a) `{2\lambda}/{\pi\varepsilon_0R}N/C`
(b) zero
(c) `{\lambda}/{\pi\varepsilon_0R}N/C`
(d) `{\lambda}/{2\pi\varepsilon_0R}N/C`
Answer (c)
NEET 2018
Question 18. The electrostatic force between the metal plates of an isolated parallel plate capacitor C having a charge Q and area A, is
(a) Independent of the distance between the plates
(b) Linearly proportional to the distance between the plates
(c) Proportional to the square root of the distance between the plates
(d) Inversely proportional to the distance between the plates
Answer (a)
Question 19. An electron falls from rest through a vertical distance h in a uniform and vertically upward directed electric field E. The direction of electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest in it through the same vertical distance h. The time of fall of the electron, in comparison to the time of fall of the proton is
(a) smaller
(b) 5 times greater
(c) 10 times greater
(d) equal
Answer (a)
Question 20. A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field `\vec{E}`. Due to the force `q\vec{E}`, its velocity increases from `0` to `6 m s^–1` in one second duration. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between `0` to `3` seconds are respectively
(a) `2ms^-1 , 4ms^-1`
(b) `1ms^-1 , 3ms^-1`
(c) `1ms^-1 , 3.5ms^-1`
(d) `1.5ms^-1 , 3ms^-1`
Answer (b)
NEET 2017
Question 21. Suppose the charge of a proton and an electron differ slightly. One of them is `-e`, the other is `(e +\Deltae)`. If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (musch greater than atomic size) apart is zero, then `\Deltae` is of the order of
[Given : mass of hydrogen `m_h = 1.67\times10^-27 kg`]
(a) `10^-23C`
(b) `10^-37C`
(c) `10^-47C`
(d) `10^20C`
Answer (b)
Question 22. A capacitor is charged by a battery. The battery is removed and another identical unchanged capacitor is connected in parallel. The total electrostatic energy of resulting system
(a) decreases by a factor of 2
(b) remains the same
(c) increases by a factor of 2
(d) increases by a factor of 4
Answer (a)
Question 23. The diagrams below show regions of equipotentials.
A positive charge is moved from A to B in each diagram.
(a) In all the four cases the work done is the same.
(b) Minimum work is required to move q in figure(l).
(c) Maximum work is required to move q in figure (II).
(d) Maximum work is required to move q in figure (III)
Answer (a)NEET 2016
Question 24. An electric dipole is placed at an angle of `30^o` with an electric field intensity `2\times10^5 N C^-1`. It experiences a torque equal to `4 N m`. The charge on the dipole, if the dipole length is `2 cm`, is
(a) `8mC`
(b) `2mC`
(c) `5mC`
(d) `7\muC`
Answer (b)
Question 25. A parallel-plate capacitor of area a, plate separation d and capacitance `C` is filled with four dielectric materials having dielectric constants `k_1, k_2, k_3` and `k_4` as shown in the figure. If a single dielectric material is to be used to have the same capacitance `C` in this capacitor, then its dielectric constant `k` is given by
(a) `k=k_1+k_2+k_3+3k_4`
(b) `k=2/3 (k_1+k_2+k_3)+2k_4`
(c) `2/k= 3/{k_1+k_2+k_3)+1/k_4`
(d) `1/k= 1/k_1+1/k_2+1/k_3+3/{2k_4}`
Answer (c)
Question 26. A capacitor of `2\muF` is charged as shown in the diagram. When the switch S is turned to position `2`, the percentage of its stored energy dissipated is
(a) `75%`
(b) `80%`
(c) `0%`
(d) `20%`
Answer (b)
Question 27. Two identical charged spheres suspended from a common point by two massless strings of lengths `l`, are initially at a distance d(d < <`l`) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity `v`. Then `v` varies as a function of the distance `x` between the spheres, as
(a) `v\propto x^{-1/2}`
(b) `v\propto x^{-1}`
(c)`v\propto x^{1/2}`
(d) `v\propto x`
Answer (a)
AIPMT 2015
Question 28. A parallel plate air capacitor has capacity C, distance of separation between plates is d and potential difference `V` is applied between the plates. Force of attraction between the plates of the parallel plate air capacitor is
(a) `{CV^2}/{d}`
(b) `{C^2V^2}/{2d^2}`
(c) `{C^2V^2}/{2d}`
(d) `{CV^2}/{2d}`
Answer (d)
Question 29. If potential (in volts) in a region is expressed as `V(x, y, z) = 6xy- y + 2yz`, the electric field (in N/C) at point `(1, 1, 0)` is
(a) `-(2\hat{i}+3\hat{j}+\hat{k})`
(b) `-(6\hat{i}+9\hat{j}+\hat{k})`
(c) `-(3\hat{i}+5\hat{j}+3\hat{k})`
(d) `-(6\hat{i}+5\hat{j}+2\hat{k})`
Answer (d)
Question 30. The electric field in a certain region is acting radially outward and is given by `E = Ar`. A charge contained in a sphere of radius 'a' centred at the origin of the field, will be given by
(a) `4\pi\varepsilon_0Aa^3`
(b) `\varepsilon_0Aa^3`
(c) `4\pi\varepsilon_0Aa^2`
(d) `A\varepsilon_0a^2`
Answer (a)
Question 31. A parallel plate air capacitor of capacitance C is connected to a cell of emf V and then disconnected from it. A dielectric slab of dieletric constant K, which can just fill the air gap of the capacitor, is now inserted in it . Which of the following is incorrect ?
(a) The change in energy stored is `1/2 CV^2 (1/K − 1)`
(b) The charge on the capacitor is not conserved.
(c) The potential difference between the plates decreases `K` times.
(c) The potential difference between the plates decreases `K` times.
(d) The energy stored in the capaciotor decreases `K` times.
Answer (b)
Question 32. In a region, the potential is represented by `V(x, y, z) = 6x-8xy-8y + 6yz,` where `V` is in volts and `x, y, z` are in metres. The electric force experienced by a charge of 2 coulomb situated at point `(1, 1, 1)` is
(a) `6\sqrt{5}N`
(b) `30N`
(c) `24N`
(d) `4\sqrt{35}N`
Answer (d)
AIPMT 2014
Question 33. A conducting sphere of radius R is given a charge Q. The electric potential and the electric field at the centre of the sphere rrespectively are
(a) zero and `Q/{4\pi\varepsilon_0R^2}`
(b) `Q/{4\pi\varepsilon_0R}` and zero
(c) `Q/{4\pi\varepsilon_0R}` and `Q/{4\pi\varepsilon_0R^2}`
(d) both are zero
Answer (b)
Question 34. Two thin dielectric slabs of dielectric constants `K_1` and `K_2(K_1` < `K_2)` are inserted between plates of a parallel plate capacitor, as shown in the figure. The variation of electric field E between the plates with distance d as measured from plate `P` is correctly shown by
(a)
(b)
(c)
(d)
Answer (c)
NEET 2013
Question 35. A charge q is placed at the centre of the line joining two equal charges Q. The system of the three charges will be in equilibrium if q is equal to
(a) `-Q/4`
(b) `Q/4`
(c) `-Q/2`
(d) `Q/2`
Answer (a)
Question 36. An electric dipole of dipole moment p is aligned parallel to a uniform electric field E. The energy required to rotate the dipole by `90^o` is
(a) `p^2 E`
(b) `pE`
(c) infinity
(d) `pE^2`
Answer (b)
Question 37. A, B and C are three points in a uniform electric field. The electric potential is
(a) maximum at C
(b) same at all three points A, B and C
(c) maximum at A
(d) maximum at B
Answer (d)
Question 38. Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is r. Now the strings are rigidly clamped at half the height. The equilibrium separation between the balls now become
(a) `({2r}/{\sqrt{3}})`
(b) `{2r}/3`
(c) `(1/\sqrt{2})^2`
(d) `(r/{2^{1/3}})`
(b) same at all three points A, B and C
(c) maximum at A
(d) maximum at B
Answer (d)
Question 38. Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is r. Now the strings are rigidly clamped at half the height. The equilibrium separation between the balls now become
(a) `({2r}/{\sqrt{3}})`
(b) `{2r}/3`
(c) `(1/\sqrt{2})^2`
(d) `(r/{2^{1/3}})`
Answer (d)
AIPMT 2012
Question 39. A parallel plate capacitor has a uniform electric field E in the space between the plates. If the distance between the plates is d and area of each plate is A, the energy stored in the capacitor is
(a) `1/2\varepsilon_0 E^2 `
(b) `{E^2 Ad}/\varepsilon_0`
(c) `1/2\varepsilon_0 E^2 Ad`
(d) `\varepsilon_0 E^2 Ad`
Answer (c)
Question 40. Two metallic spheres of radii `1 cm` and `3 cm` are given charges of `-1\times10^-2` and `5\times10^-2C`, respectively. If these are connected by a conducting wire, the final charge on the bigger sphere is
(a) `2\times10^-2 C`
(b) `3\times10^-2 C`
(c) `4\times10^-2 C`
(d) `1\times10^-2 C`
Answer (b)
Question 41. An electric dipole of moment p is placed in an electric field of intensity E. The dipole acquires a position such that the axis of the dipole makes an angle `\theta` with the direction of the field. Assuming that the potential energy of the dipole to be zero when `\theta= 90^o`, the torque and the potential energy of the dipole will respectively be
(a) `pEsin\theta, -pEcos\theta`
(b) `pEsin\theta, -2pEcos\theta`
(c) `pEsin\theta, 2pEcos\theta`
(d) `pEcos\theta, -pEsin\theta`
Answer (a)
(a) `{3qQ}/{4\pi\varepsilon_0a}`
(a) `2\times10^-2 C`
(b) `3\times10^-2 C`
(c) `4\times10^-2 C`
(d) `1\times10^-2 C`
Answer (b)
Question 41. An electric dipole of moment p is placed in an electric field of intensity E. The dipole acquires a position such that the axis of the dipole makes an angle `\theta` with the direction of the field. Assuming that the potential energy of the dipole to be zero when `\theta= 90^o`, the torque and the potential energy of the dipole will respectively be
(a) `pEsin\theta, -pEcos\theta`
(b) `pEsin\theta, -2pEcos\theta`
(c) `pEsin\theta, 2pEcos\theta`
(d) `pEcos\theta, -pEsin\theta`
Answer (a)
Question 42. What is the flux through a cube of side `a` if a point charge of q is at one of its corner?
(a) `{2q}/\varepsilon_0`
(b) `{q}/{8\varepsilon_0}`
(c) `{q}/\varepsilon_0`
(d) `{q}/{2\varepsilon_0}6a^2`
Answer (b)
Question 43. Four point charges `-Q, -q, 2q` and `2Q` are placed, one at each corner of the square. The relation between `Q` and `q` for which the potential at the centre of the square is zero is
(a) `Q=-q`
(b) `Q=-1/q`
(c) `Q=q`
(d) `Q=1/q`
Answer (a)
AIPMT 2011
Question 44. The electric potential V at any point `(x, y, z)`, all in metres in space is given by `V = 4x^2` volt. The electric field at the point `(1, 0, 2)` in volt/meter, is
(a) 8 along negative X-axis
(b) 8 along positive X-axis
(c) 16 along negative X-axis
(d) 16 along positive X-axis
Answer (a)
Question 45. Three charges, each `+q`, are placed at the corners of an isosceles triangle `ABC` of sides `BC` and `AC`, `2a`. `D` and `E` are the mid points of `BC` and `CA`. The work done in taking a charge `Q` from `D` to `E` is(a) `{2q}/\varepsilon_0`
(b) `{q}/{8\varepsilon_0}`
(c) `{q}/\varepsilon_0`
(d) `{q}/{2\varepsilon_0}6a^2`
Answer (b)
Question 43. Four point charges `-Q, -q, 2q` and `2Q` are placed, one at each corner of the square. The relation between `Q` and `q` for which the potential at the centre of the square is zero is
(a) `Q=-q`
(b) `Q=-1/q`
(c) `Q=q`
(d) `Q=1/q`
Answer (a)
AIPMT 2011
Question 44. The electric potential V at any point `(x, y, z)`, all in metres in space is given by `V = 4x^2` volt. The electric field at the point `(1, 0, 2)` in volt/meter, is
(a) 8 along negative X-axis
(b) 8 along positive X-axis
(c) 16 along negative X-axis
(d) 16 along positive X-axis
Answer (a)
(a) `{3qQ}/{4\pi\varepsilon_0a}`
(b) `{3qQ}/{8\pi\varepsilon_0a}`
(c) `{qQ}/{4\pi\varepsilon_0a}`
(d) zero
Answer (d)
Question 46. A parallel plate capacitor has a uniform electric field E in the space between the plates. If the distance between the plates is d and area of each plate is A, the energy stored in the capacitor isAnswer (d)
(a) `1/2 \varepsilon_0E^2`
(b) `{E^2 Ad}/\varepsilon_0`
(c) `1/2 \varepsilon_0E^2Ad`
(d) `\varepsilon_0 EAd`
Answer (c)
Question 47. Four electric charges `+q, +q, -q` and `-q` are placed at the corners of a square of side `2L` (see figure). The electric potential at point A, midway between the two charges `+ q` and `+q`, is
(a) `1/{4\pi\varepsilon_0}{2q}/L (1+\sqrt{5})`
(b) `1/{4\pi\varepsilon_0}{2q}/L (1+1/\sqrt{5})`
(c) `1/{4\pi\varepsilon_0}{2q}/L (1-1/\sqrt{5})`
(d) zero
Answer (c)
Question 48. A charge Q is enclosed by a Gaussian spherical surface of radius R. If the radius is doubled, then the outward electric flux will
(a) increase four times
(b) be reduced to half
(c) remain the same
(d) be doubled
Answer (c)
AIPMT 2010
Question 49. Two parallel metal plates having charges `+Q` and `-Q` face each other at a certain distance between them. If the plates are now dipped in kerosene oil tank, the electric field between the plates will
(a) become zero
(b) increase
(c) decrease
(d) remain same
Answer (c)
Question 50. The electric field at a distance `{3R}/2` from the centre of a charged conducting spherical shell of radius R is E. The electric field at a distance `R/2` from the centre of the sphere is
(a) zero
(b) E
(c) `E/2`
(d) `E/3`
Answer (a)
Question 51. A square surface of side L meter in the plane of the paper is placed in a uniform electric field `E`(volt/m) acting along the same plane at an angle `\theta` with the horizontal side of the square as shown in figurre.
The electric flux linked to the surface, in units of volt m is
(a) `EL^2`
(b) `EL^2cos\theta`
(c) `EL^2sin\theta`
(d) zero
Answer (d)
Question 52. Two positives ions, each carrying a charge q, are separated by a distance d. If F is the force of repulsion between the ions, the number of electrons missing from each ion will be (e being the charge on an electron)
(a) `{4\pi\varepsilon_0Fd^2}/{e^2}`
(b) `\sqrt{{4\pi\varepsilon_0Fe^2}/{d^2}}`
(c) `\sqrt{{4\pi\varepsilon_0Fd^2}/{e^2}}`
(d) `{4\pi\varepsilon_0Fd^2}/{q^2}`
Answer (c)
Question 53. A series combination of `n_1` capacitors, each of value `C_1`, is charged by a source of potential difference `4V`. When another parallel combination of `n_2` capacitors, each of value `C_2`, is charged by a source of potential difference `V`, it has the same (total) energy stored in it. as the first combination has. The value of `C_2`. in terms of `C_1`, is then
(a) `{2C_1}/{n_1n_2}`
(b) `16n_2/n_1C_1`
(c) `2n_2/n_1C_1`
Answer (c)
Question 47. Four electric charges `+q, +q, -q` and `-q` are placed at the corners of a square of side `2L` (see figure). The electric potential at point A, midway between the two charges `+ q` and `+q`, is
(a) `1/{4\pi\varepsilon_0}{2q}/L (1+\sqrt{5})`
(b) `1/{4\pi\varepsilon_0}{2q}/L (1+1/\sqrt{5})`
(c) `1/{4\pi\varepsilon_0}{2q}/L (1-1/\sqrt{5})`
(d) zero
Answer (c)
Question 48. A charge Q is enclosed by a Gaussian spherical surface of radius R. If the radius is doubled, then the outward electric flux will
(a) increase four times
(b) be reduced to half
(c) remain the same
(d) be doubled
Answer (c)
AIPMT 2010
Question 49. Two parallel metal plates having charges `+Q` and `-Q` face each other at a certain distance between them. If the plates are now dipped in kerosene oil tank, the electric field between the plates will
(a) become zero
(b) increase
(c) decrease
(d) remain same
Answer (c)
Question 50. The electric field at a distance `{3R}/2` from the centre of a charged conducting spherical shell of radius R is E. The electric field at a distance `R/2` from the centre of the sphere is
(a) zero
(b) E
(c) `E/2`
(d) `E/3`
Answer (a)
Question 51. A square surface of side L meter in the plane of the paper is placed in a uniform electric field `E`(volt/m) acting along the same plane at an angle `\theta` with the horizontal side of the square as shown in figurre.
(a) `EL^2`
(b) `EL^2cos\theta`
(c) `EL^2sin\theta`
(d) zero
Answer (d)
Question 52. Two positives ions, each carrying a charge q, are separated by a distance d. If F is the force of repulsion between the ions, the number of electrons missing from each ion will be (e being the charge on an electron)
(a) `{4\pi\varepsilon_0Fd^2}/{e^2}`
(b) `\sqrt{{4\pi\varepsilon_0Fe^2}/{d^2}}`
(c) `\sqrt{{4\pi\varepsilon_0Fd^2}/{e^2}}`
(d) `{4\pi\varepsilon_0Fd^2}/{q^2}`
Answer (c)
Question 53. A series combination of `n_1` capacitors, each of value `C_1`, is charged by a source of potential difference `4V`. When another parallel combination of `n_2` capacitors, each of value `C_2`, is charged by a source of potential difference `V`, it has the same (total) energy stored in it. as the first combination has. The value of `C_2`. in terms of `C_1`, is then
(a) `{2C_1}/{n_1n_2}`
(b) `16n_2/n_1C_1`
(c) `2n_2/n_1C_1`
(d) `{16C_1}/{n_1n_2}`
Answer (d)
AIPMT 2009
Question 54. Three concentric spherical shells have radii a, b and c (a < b < c) anf have surface charge densities `\sigma, -\sigma` and `\sigma`, respectively. If `V_A, V_B` and `V_C` denote the potentials of the three shells, then, for `c = a + b,` we have
(a) `V_C=V_B\neV_A`
(b) `V_C\neV_B\ne V_A`
(c) `V_C=V_B= V_A`
(d) `V_C=V_A\ne V_B`
Answer (d)
Question 55. Three capacitors each of capacitance C and of breakdown voltage V are joined in series. The capacitance and breakdown voltages of the combination will be
(a) `3C, V/3`
(b) `C/3, 3V`
(c) `3C, 3V`
(d) `C/3, V/3`
Answer (b)
Question 56. The electric potential at a point `(x, y, z)` is given by `V =- x^2y-xz^3 + 4`
The electric field at that point is
(a) `\vec{E}=\hat{i}2xy+\hat{j}(x^2+y^2)+\hat{k}(3xz-y^2)`
(b) `\vec{E}=\hat{i}z^3+\hat{j}xyz+\hat{k}z^2`
(c) `\vec{E}=\hat{i}(2xy-z^3)+\hat{j}xy^2+\hat{k}3z^2x`
(d) `\vec{E}=\hat{i}(2xy+z^3)+\hat{j}x^2+\hat{k}3z^2x`
Answer (d)
AIPMT 2008
Question 57. A parallel plate capacitor has a uniform electric field E in the space between the plates. If the distance between the plates is d and area of each plate is A, the energy stored in the capacitor is
(a) `1/2\varepsilon_0E^2`
(b) `{E^2Ad}/\varepsilon_0`
(c) `1/2\varepsilon_0E^2Ad`
(d) `\varepsilon_0EAd`
Answer (c)
Question 58. The electric potential at a point in free space due to charge `Q` coulomb is `Q\times10^11` volts. The electric field at that point is
(a) `4\pi\varepsilon_0Q\times10^20 Vm^-1`
(b) `12\pi\varepsilon_0Q\times10^22 Vm^-1`
(c) `4\pi\varepsilon_0Q\times10^22 Vm^-1`
(d) `12\pi\varepsilon_0Q\times10^20 Vm^-1`
Answer (c)
Question 59. A thin conducting ring of radius R is given a charge `+Q`. The electric field at the centre `O` of the ring due to the charge on the part `AKB` of the ring is `E`. The electric field at the centre due to the charge on the part `ACDB` of the ring is
(a) E along KO
(b) 3E along OK
(c) 3E along KO
(d) E along OK
Answer (d)
AIPMT 2007
Question 60. Charges `+q` and `-q` are placed at points A and B respectively which are a distance `2L` apart, C is the midnight between A and B. The work done in moving a charge `+ Q` along the semicircle CRD is
(a) E along KO
(b) 3E along OK
(c) 3E along KO
(d) E along OK
Answer (d)
AIPMT 2007
(a) `{qQ}/{2\pi\varepsilon_0L}`
(b) `{qQ}/{6\pi\varepsilon_0L}`
(c) `-{qQ}/{6\pi\varepsilon_0L}`
(d) `{qQ}/{4\pi\varepsilon_0L}`
Answer (c)
Question 61. A hollow cylinder has a charge q coulomb within it. If `f` is the electric flux in units of voltmeter associated with the curved surface B, the flux linked with the plane surface A in units of `V-m` will be
(a) `q/{2\varepsilon_0}`
(b) `\phi/3`
(c) `q/{\varepsilon_0}-\phi`
(d) `1/2(q/{\varepsilon_0}-\phi)`
Answer (d)
Question 62. Three point charges `+q, -2q` and `+ q` are placed at points `(x = 0, y = a, z = 0), (x = 0, y = 0, z = 0)` and `(x = a, y = 0, z = 0)` respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are
(a) `\sqrt{2}qa` along the joining points `(x=0, y=0, z=0)` and `(x=a, y=a, z=0)`
(b) `qa` along the joining points `(x=0, y=0, z=0)` and `(x=a, y=a, z=0)`
(c) `\sqrt{2}qa` along `+x` direction
(d) `\sqrt{2}qa` along `+y` direction
Answer (a)
Question 63. Two condensers, one of capacity `C` and other of capacity `C/2` are connected to a V-volt battery, as shown in the figure. The work done in charging fully both the condensers is
(a) `1/4CV^2`
(b) `3/4CV^2`
(c) `1/2CV^2`
(d) `2CV^2`
Answer (b)
AIPMT 2006
Question 64. A parallel plate air capacitor is charged to a potential difference of V volts. After disconnecting the charging battery the distance between the plates of the capacitor is increased using an insulting handle. As a result the potential difference between the plates
(a) increases
(b) decreases
(c) does not charge
(d) becomes zero
Answer (a)
Question 65. An electric dipole of moment `\vec{p}` is lying along a uniform electric field `\vec{E}`. The work done in rotating the dipole by `90^o` is
(a) `pE`
(b) `\sqrt{2}pE`
(c) `{pE}/2`
(d) `2pE`
Answer (a)
Question 66. A square surface of side L metres is in the plane of the paper. A uniform electric field `\vec{E}` (volt/m), also in the plane of the paper is limited only to the lower half of the square surface (see figure). The electric flux in SI inits associated with the surface is
(a) `EL^2`
(b) `{EL^2}/{2\varepsilon_0}`
(c) `{EL^2}/2`
(d) zero
Answer (d)
AIPMT 2005
(a) zero
(b) `({qQ}/{4\pi\varepsilon_0}1/a^2).\sqrt{2}a`
(c) `({-qQ}/{4\pi\varepsilon_0}1/a^2).\sqrt{2}a`
(d) `({qQ}/{4\pi\varepsilon_0}1/a^2).a/\sqrt{2}`
Answer (a)
AIPMT 2004
Question 70. A bullet of mass `2 g` is having a charge of `2\muC`. Through what potential difference must it be accelerated, starting from rst, to acquire a speed of `10 m/s` ?
(a) `5KV`
(b) `50KV`
(c) `5V`
(d) `50V`
Answer (b)
Question 71. An electric dipole has the magnitude of its charge as q and its dipole moment is p. It is placed in a uniform electric field E. If its dipole moment is along the direction of the field, the force on it and its potential energy are respectively
(a) `2qE` and minimum
(b) `q.E & p.E`
(c) zero and minimum
(d) `q.E` and maximum
Answer (c)
AIPMT 2003
Question 72. Three capacitors each of capacity `4\muF` are to be connected in such a way that the effective capacitance is `6\muF` This can be done by
(a) connecting all of them in series
(b) connecting them in parallel
(c) connecting two in series and one in oarallel
(d) connecting two in parallel and one in series
Answer (c)
Question 73. A charge q is located at the centre of a cube. The electric flux through any face is
(a) `{2\piq}/{6(4\pi\varepsilon_0)}`
(b) `{4\piq}/{6(4\pi\varepsilon_0)}`
(c) `{\piq}/{6(4\pi\varepsilon_0)}`
(d) `{q}/{6(4\pi\varepsilon_0)}`
Answer (b)
AIPMT 2002
Question 74. Identical charges `(-q)` are placed at each corners of cube of side b then electrostatic potential energy of charge `(+q)` which is placed at centre of cube will be
(a) `{-4\sqrt{2}q^2}/{\pi\varepsilon_0b}`
(b) `{-8\sqrt{2}q^2}/{\pi\varepsilon_0b}`
(c) `{-4q^2}/{\sqrt{3}\pi\varepsilon_0b}`
(d) `{-8\sqrt{2}q^2}/{4\pi\varepsilon_0b}`
Answer (c)
Question 75. Some charge is being given to a conductor. Then its potential is
(a) maximum at surface
(b) maximum at center
(c) remain same throughout the conductor
(d) maximum somewhere between surface and centre
Answer (c)
Question 76. A capacitor of capacity `C_1` charged upto `V` volt and then connected to an uncharged capacitor of capacity `C_2`. The final potential difference across each will be
(a) `{C_1V}/{C_1+C_2}`
(b) `{C_2V}/{C_1+C_2}`
(c) `(1-C_2/C_1)V`
(d) `(1+C_2/C_1)`
Answer (a)
AIPMT 2001
Question 77. A dipole of dipole moment `\vec{p}` is placed in uniform electric field `\vec{E}` then torque acting on it is given by
(a) `\vec{\tau}=\vec{p}.\vec{E}`
(b) `\vec{\tau}=\vec{p}\times\vec{E}`
(c) `\vec{\tau}=\vec{p}+\vec{E}`
(b) `Q/{6\varepsilon_0}\times10^-3`
(c) `Q/{24\varepsilon_0}`
(d) `Q/{8\varepsilon_0}`
Answer (a)
Question 79. Energy per unit volume for a capacitor having area A and separation d kept at potential difference V is given by
(a) `1/2\varepsilon_0V^2/d^2`
(b) `1/{2\varepsilon_0}V^2/d^2`
(c) `1/2 C^2V^2`
(d) `Q^2/{2C}`
Answer (a)
AIPMT 2000
Question 80. A charge Q is situated at the corner of a cube, the electric flux passed through all the six faces of the cube is
(a) `Q/{6\varepsilon_0}`
(b) `Q/{8\varepsilon_0}`
(c) `Q/{\varepsilon_0}`
(d) `Q/{2\varepsilon_0}`
Answer (c)
Question 81. Electric field at centre `O` of semicircle of radius `a` having linear charge density `\lambda` given as
(a) `{2\lambda}/{\varepsilon_0a}`
(b) `{\lambda\pi}/{\varepsilon_0a}`
(c) `{\lambda}/{2\pi\varepsilon_0a}`
(d) `{\lambda}/{\pi\varepsilon_0a}`
Answer (c)
Answer (c)
Question 61. A hollow cylinder has a charge q coulomb within it. If `f` is the electric flux in units of voltmeter associated with the curved surface B, the flux linked with the plane surface A in units of `V-m` will be
(a) `q/{2\varepsilon_0}`
(b) `\phi/3`
(c) `q/{\varepsilon_0}-\phi`
(d) `1/2(q/{\varepsilon_0}-\phi)`
Answer (d)
Question 62. Three point charges `+q, -2q` and `+ q` are placed at points `(x = 0, y = a, z = 0), (x = 0, y = 0, z = 0)` and `(x = a, y = 0, z = 0)` respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are
(a) `\sqrt{2}qa` along the joining points `(x=0, y=0, z=0)` and `(x=a, y=a, z=0)`
(b) `qa` along the joining points `(x=0, y=0, z=0)` and `(x=a, y=a, z=0)`
(c) `\sqrt{2}qa` along `+x` direction
(d) `\sqrt{2}qa` along `+y` direction
Answer (a)
Question 63. Two condensers, one of capacity `C` and other of capacity `C/2` are connected to a V-volt battery, as shown in the figure. The work done in charging fully both the condensers is
(a) `1/4CV^2`
(b) `3/4CV^2`
(c) `1/2CV^2`
(d) `2CV^2`
Answer (b)
AIPMT 2006
Question 64. A parallel plate air capacitor is charged to a potential difference of V volts. After disconnecting the charging battery the distance between the plates of the capacitor is increased using an insulting handle. As a result the potential difference between the plates
(a) increases
(b) decreases
(c) does not charge
(d) becomes zero
Answer (a)
Question 65. An electric dipole of moment `\vec{p}` is lying along a uniform electric field `\vec{E}`. The work done in rotating the dipole by `90^o` is
(a) `pE`
(b) `\sqrt{2}pE`
(c) `{pE}/2`
(d) `2pE`
Answer (a)
Question 66. A square surface of side L metres is in the plane of the paper. A uniform electric field `\vec{E}` (volt/m), also in the plane of the paper is limited only to the lower half of the square surface (see figure). The electric flux in SI inits associated with the surface is
(a) `EL^2`
(b) `{EL^2}/{2\varepsilon_0}`
(c) `{EL^2}/2`
(d) zero
Answer (d)
AIPMT 2005
Question 67. A network of four capacitors of capacity equal to `C_1 = C, C_2 = 2C, C_3 = 3C` and `C_4 = 4C` are connected to a battery as shown in the figure. The ratio of the charges on `C_2` and `C_4` is
(a) `4/7`
(b) `3/{22}`
(c) `7/4`
(d) `{22}/3`
Answer (b)
Question 68. Two charges `q_1` and `q_2` are placed `30 cm` apart, as shown in the figure. A third charge `q_3` is moved along the arc of a circle of radius `40 cm` from C to D.
(a) `4/7`
(b) `3/{22}`
(c) `7/4`
(d) `{22}/3`
Answer (b)
The change in the potential energy of the system is `kq_3/{4\pi\varepsilon_0}` where k is
(a) `8q_1`
(b) `6q_1`
(c) `8q_2`
(d) `6q_2`
Answer (c)
Question 69. As per the diagram a point charge `+q` is placed at the origin O. Work done in taking another point charge `-Q` from the point A [coordinates `(0, a)`] to another point B `[(a,0)]` along the path `AB`
(a) `8q_1`
(b) `6q_1`
(c) `8q_2`
(d) `6q_2`
Answer (c)
(a) zero
(b) `({qQ}/{4\pi\varepsilon_0}1/a^2).\sqrt{2}a`
(c) `({-qQ}/{4\pi\varepsilon_0}1/a^2).\sqrt{2}a`
(d) `({qQ}/{4\pi\varepsilon_0}1/a^2).a/\sqrt{2}`
Answer (a)
AIPMT 2004
Question 70. A bullet of mass `2 g` is having a charge of `2\muC`. Through what potential difference must it be accelerated, starting from rst, to acquire a speed of `10 m/s` ?
(a) `5KV`
(b) `50KV`
(c) `5V`
(d) `50V`
Answer (b)
Question 71. An electric dipole has the magnitude of its charge as q and its dipole moment is p. It is placed in a uniform electric field E. If its dipole moment is along the direction of the field, the force on it and its potential energy are respectively
(a) `2qE` and minimum
(b) `q.E & p.E`
(c) zero and minimum
(d) `q.E` and maximum
Answer (c)
AIPMT 2003
Question 72. Three capacitors each of capacity `4\muF` are to be connected in such a way that the effective capacitance is `6\muF` This can be done by
(a) connecting all of them in series
(b) connecting them in parallel
(c) connecting two in series and one in oarallel
(d) connecting two in parallel and one in series
Answer (c)
Question 73. A charge q is located at the centre of a cube. The electric flux through any face is
(a) `{2\piq}/{6(4\pi\varepsilon_0)}`
(b) `{4\piq}/{6(4\pi\varepsilon_0)}`
(c) `{\piq}/{6(4\pi\varepsilon_0)}`
(d) `{q}/{6(4\pi\varepsilon_0)}`
Answer (b)
AIPMT 2002
Question 74. Identical charges `(-q)` are placed at each corners of cube of side b then electrostatic potential energy of charge `(+q)` which is placed at centre of cube will be
(a) `{-4\sqrt{2}q^2}/{\pi\varepsilon_0b}`
(b) `{-8\sqrt{2}q^2}/{\pi\varepsilon_0b}`
(c) `{-4q^2}/{\sqrt{3}\pi\varepsilon_0b}`
(d) `{-8\sqrt{2}q^2}/{4\pi\varepsilon_0b}`
Answer (c)
Question 75. Some charge is being given to a conductor. Then its potential is
(a) maximum at surface
(b) maximum at center
(c) remain same throughout the conductor
(d) maximum somewhere between surface and centre
Answer (c)
Question 76. A capacitor of capacity `C_1` charged upto `V` volt and then connected to an uncharged capacitor of capacity `C_2`. The final potential difference across each will be
(a) `{C_1V}/{C_1+C_2}`
(b) `{C_2V}/{C_1+C_2}`
(c) `(1-C_2/C_1)V`
(d) `(1+C_2/C_1)`
Answer (a)
AIPMT 2001
Question 77. A dipole of dipole moment `\vec{p}` is placed in uniform electric field `\vec{E}` then torque acting on it is given by
(a) `\vec{\tau}=\vec{p}.\vec{E}`
(b) `\vec{\tau}=\vec{p}\times\vec{E}`
(c) `\vec{\tau}=\vec{p}+\vec{E}`
(d) `\vec{\tau}=\vec{p}-\vec{E}`
Answer (b)
Question 78. A charge `Q\muC` is placed at the centre of a cube, the flux coming out from each face will be
(a) `Q/{6\varepsilon_0}\times10^-6`
Answer (b)
Question 78. A charge `Q\muC` is placed at the centre of a cube, the flux coming out from each face will be
(a) `Q/{6\varepsilon_0}\times10^-6`
(b) `Q/{6\varepsilon_0}\times10^-3`
(c) `Q/{24\varepsilon_0}`
(d) `Q/{8\varepsilon_0}`
Answer (a)
Question 79. Energy per unit volume for a capacitor having area A and separation d kept at potential difference V is given by
(a) `1/2\varepsilon_0V^2/d^2`
(b) `1/{2\varepsilon_0}V^2/d^2`
(c) `1/2 C^2V^2`
(d) `Q^2/{2C}`
Answer (a)
AIPMT 2000
Question 80. A charge Q is situated at the corner of a cube, the electric flux passed through all the six faces of the cube is
(a) `Q/{6\varepsilon_0}`
(b) `Q/{8\varepsilon_0}`
(c) `Q/{\varepsilon_0}`
(d) `Q/{2\varepsilon_0}`
Answer (c)
Question 81. Electric field at centre `O` of semicircle of radius `a` having linear charge density `\lambda` given as
(a) `{2\lambda}/{\varepsilon_0a}`
(b) `{\lambda\pi}/{\varepsilon_0a}`
(c) `{\lambda}/{2\pi\varepsilon_0a}`
(d) `{\lambda}/{\pi\varepsilon_0a}`
Answer (c)
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