Electrostatics PYQs Set 2 (PDF)

Set 2 of 13 · Questions 31-60 of 385

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Mere Teacher · Previous Year Questions JEE Main Physics · Electrostatics · Set 2 (Q31-60)
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31. $A parallel plate air capacitor has capacity C farad, potential V volt and energy E joule. When the gap between the plates is completely filled with dielectric$ (1) $both V and E increase$ (2) $Both V and E decrease$ (3) $V decreases, E increases$ (4) $V increases, E decreases$ 32. $In bringing an electron towards another electron, the electrostatic potential energy of the system$ (1) $becomes zero$ (2) $increases$ (3) $decreases$ (4) $remains same$ 33. $An electron falls from rest through a vertical distance h in a uniform and vertically upward directed electric field E. The direction of electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest in it through the same vertical distance h. The time of fall of the electron, in comparison to the time of falls of the proton is:$ (1) $smaller$ (2) $equal$ (3) $10 times greater$ (4) $5 times greater$ 34. $The electric field intensity on the surface of a solid charged sphere of radius ' r ' and volume charge density ' Q ' is (c_{0} = permittivity of free space)$ (1) $\frac{ρr}{3 ϵ _{0}}$ (2) $\frac{ρ}{4 π ϵ _{0} ^{r}}$ (3) $zero$ (4) $\frac{5 ρr}{6 ϵ _{0}}$ 35. $A particle of mass m and charge q is placed at rest in uniform electric field E and then released. The kinetic energy attained by the particle after moving a distance y is$ (1) $qEy$ (2) $qE y^{2}$ (3) $q^{2} Ey$ (4) $q E^{2} y$ 36. $A 1µC charge is divided into two parts and placed at 1 cm distance so that the repulsive force between them is maximum. The charges of the two parts are:$ (1) $7µC,3µC$ (2) $8µC 2µC$ (3) $5µC,5µC$ (4) $9µC,1µC$ 37. $A dipole of dipole moment P and moment of inertia I is placed in a uniform electric field E . If it is displaced slightly from its stable equilibrium position, the period of oscillation of dipole is$ (1) $\frac{1}{2 π} \frac{PE}{I}$ (2) $π \frac{I}{PE}$ (3) $\frac{PE}{I}$ (4) $2 π \frac{I}{PE}$ 38. $Two charges of each magnitude 0. 01 C and separated by a distance of 0. 4 mm constitute an electric dipole. If the dipole is placed in an uniform electric field E of 10 dyne. C^{- 1} making 30° angle with E, the magnitude of torque acting on dipole is:$ (1) $4.0 x 1 0^{- 10} Nm$ (2) $1.0 x 1 0^{- 8} Nm$ (3) $1.5 x 1 0^{- 9} Nm$ (4) $2.0 x 1 0^{- 10} N m$ 39. $An electric field is given by (6 i + 5 j + 3 k) N / C . The electric flux through a surface area 30 i m^{2} lying in YZ - plane (in SI unit) is:$ (1) $90$ (2) $150$ (3) $180$ (4) $60$ 40. $An electron of mass ' m ' and charge ' q ' is accelerated from rest in a uniform electric field of strength ' E'. The velocity acquired by it as it travels a distance ' l ' is$ (1) $(\frac{2 Eql}{m})^{1/2}$ (2) $(\frac{2 Eq}{ml})^{1/2}$ (3) $(\frac{2 Em}{ql})^{1/2}$ (4) $(\frac{Eq}{ml})^{1/2}$ 41. $A voltmeter reads 4 V when connected to a parallel plate capacitor with air as a dielectric. When a dielectric slab is introduced between plates for the same configuration, voltmeter reads 2 V. What is the dielectric constant of the material?$ (1) $8$ (2) $0.5$ (3) $10$ (4) $2$ 42. $Statement (A): Inside a charged hollow metal sphere, E = 0, V \neq = 0 . (E-electric field, V - electric potential) Statement (B): The work done in moving a positive charge on an equipotential surface is zero.Statement (C): When two like charges are brought closer, their mutual electrostatic potential energy will increase.$ (1) $A, B, C are true$ (2) $A, B are true, C is false$ (3) $A, C are true, B is false$ (4) $B, C are true, A is false$ 43. $Given below are two statements: one is labelled as Assertion (A)and the other is labelled as Reason (R). Assertion (A): The outer body of an aircraft is made of metal which protects persons sitting inside from lightning strikes. Reason (R): The electric field inside the cavity enclosed by a conductor is zero. In the light of the above statements, choose the most appropriate answer from the options given below:$ (1) $Both (A) and (R) are correct but (R) is not the correct explanation of (A)$ (2) $(A) is correct but (R) is not correct$ (3) $Both (A) and (R) are correct and (R) is the correct explanation of (A)$ (4) $(A) is not correct but (R) is correct$ 44. $For a uniformly charged ring of radius R, the electric field on its axis has the largest magnitude at a distance h from its centre. Then value of h is:$ (1) $\frac{R}{2}$ (2) $R$ (3) $\frac{R}{5}$ (4) $R 2$ 45. $An electric dipole of dipole moment p is aligned parallel to a uniform electric field E . The energy required to rotate the dipole by 9 0^{o} is$ (1) $p^{2} E$ (2) $pE$ (3) $infinity$ (4) $p E^{2}$ 46. $In a space having electric field E = A (x i + y j) the potential at a point (10 m, 20 m) is zero, then the potential at the origin is (A = 10 Vm^{- 2})]$ (1) $500 V .$ (2) $2000 V$ (3) $2500 V$ (4) $1500 V$ 47. $An electric field of 1000 V/m is applied to an electric dipole at angle of 45°. The value of electric dipole moment is 10^{- 29} C.m. What is the potential energy of the electric dipole?$ (1) $- 20 \times 10^{- 18} J$ (2) $- 7 \times 10^{- 27} J$ (3) $- 10 \times 10^{- 29} J$ (4) $- 9 \times 10^{- 20} J$ 48. $The electrostatic potential on the surface of uniformly charged spherical shell of radius R = 10 cm is 120 V. The potential at the centre of shell, at a distance r = 5 cm from center, and at a distance r = 15 cm from the centre of the shell respectively, are:$ (1) $0 V, 120 V, 40 V$ (2) $120 V, 120 V, 80 V$ (3) $40 V, 40 V, 80 V$ (4) $0 V, 0 V, 80 V$ 49. $Sixty four conducting drops each of radius 0.02 m and each carrying a charge of 5µC are combined to form a bigger drop. The ratio of surface density of bigger drop to the smaller drop will be:$ (1) $1 : 4$ (2) $4 : 1$ (3) $1 : 8$ (4) $8 : 1$ 50. $Two spheres of electric charges + 2 nC and - 8 nC are placed at a distance d apart. If they are allowed to touch each other, what is the new distance between them to get a repulsive force of same magnitude as before?$ (1) $\frac{d}{2}$ (2) $d$ (3) $\frac{3 d}{4}$ (4) $\frac{4 d}{3}$ 51. $A parallel-plate capacitor of plate area 10 cm^{2} and plate separation 3 mm is charged to a potential difference 12 V and then the battery is disconnected. A slab of dielectric constant 3 is then inserted between the plates. The work done on the system in the process of inserting the slab is α ϵ_{0} . The value of α is (Take ϵ_{0} as the permittivity of free space)$ (1) $8$ (2) $12$ (3) $16$ (4) $18$ 52. $The electric field and the potential of an electric dipole (along it's axis) vary with distance r, respectively as$ (1) $\frac{1}{r ^{2}} and \frac{1}{r ^{3}}$ (2) $\frac{1}{r} and \frac{1}{r ^{2}}$ (3) $\frac{1}{r ^{3}} and \frac{1}{r ^{2}}$ (4) $\frac{1}{r ^{2}} and \frac{1}{r}$ 53. $Two positive ions, each carrying a charge q, are separated by a distance d . If F is the force of repulsion between the ions, the number of electrons missing from each ion will be (e being the charge on an electron)$ (1) $\frac{4 π ϵ _{0} F d ^{2}}{e ^{2}}$ (2) $\frac{4 π ϵ _{0} F e ^{2}}{d ^{2}}$ (3) $\frac{4 π ϵ _{0} F d ^{2}}{e ^{2}}$ (4) $\frac{4 π ϵ _{0} F d ^{2}}{q ^{2}}$ 54. $An electron falls from rest through a vertical distance h in a uniform and vertically upward directed electric field E. The direction of electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest in it through the same vertical distance h. The time of fall of the electron, in comparison to the time of fall of the proton is [NEET 2018]$ (1) $10 times greater$ (2) $5 times greater$ (3) $smaller$ (4) $equal$ 55. $Ten charges are placed on the circumference of a circle of radius R with constant angular separation between successive charges. Alternate charges 1, 3, 5, 7, 9 have charge (+ q) each, while 2, 4, 6, 8, 10 have charge (- q) each. The potential V and the electric field E at the center of the circle are respectively (Take V = 0 at infinity)$ (1) $V = 0; E = 0$ (2) $V = \frac{10 q}{4 π ϵ _{0} R}; E = \frac{10 q}{4 π ϵ _{0} R ^{2}}$ (3) $V = \frac{10 q}{4 π ϵ _{0} R}; E = 0$ (4) $V=5q4πε0R;E=0$ 56. $An electron of mass ' m_{e}' and a proton of mass ' m', are kept in a uniform electric field. The ratio of the acceleration of electron (a_{e}) to the acceleration of proton (a_{p}) is$ (1) $infinity$ (2) $\frac{m _{p}}{m _{e}}$ (3) $one$ (4) $\frac{m _{e}}{m _{p}}$ 57. $27 identical drops are charged at 22V each. They combine to form a bigger drop. The potential of the bigger drop will be____V.$ 58. $Two electric dipoles of dipole moments 1.2 x 10-30 cm and 2.4 x 10-30 cm are placed in two difference uniform electric fields of strengths 5 x 1 0^{4} NC-1 and 15 x 104 NC-1 respectively. The ratio of maximum torque experienced by the electric dipoles will be \frac{1}{x} . The value of x is ____ .$ 59. $An electric field, E = \frac{2 i + 6 j + 8 k}{6} passes through the surface of 4 m^{2} area having unit vector n = (\frac{2 i + j + k}{6}) . The electric flux for that surface is_____ Vm.$ 60. $An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet S having surface charge density +σ. The electron at t = 0 is at a distance of 1 m from S and has a speed of 1 m / s . The maximum value of σ if the electron strikes S at t = 1 s is α (\frac{m ϵ _{0}}{e}) \frac{C}{m ^{2}} the value of α is$