Electrostatics PYQs Set 3 (PDF)

Set 3 of 13 · Questions 61-90 of 385

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Mere Teacher · Previous Year Questions JEE Main Physics · Electrostatics · Set 3 (Q61-90)
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61. $Given below are two statements. Statement I: Electric potential is constant within and at the surface of each conductor. Statement II: Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point. In the light of the above statements, choose the most appropriate answer from the options give below.$ (1) $Both statement I and statement II are correct$ (2) $Both statement I and statement II are incorrect$ (3) $Statement I is correct but statement II is incorrect$ (4) $Statement I is incorrect but and statement II is correct$ 62. $In a region, the intensity of an electric field is given by E = (2 i + 3 j + k) N C^{- 1} . The electric flux through a surface of area 10 i m^{2} in the region is$ (1) $5 Nm^{2} C^{- 1}$ (2) $10 Nm^{2} C^{- 1}$ (3) $15 Nm^{2} C^{- 1}$ (4) $20 Nm^{2} C^{- 1}$ 63. $Two charges 7 μC and - 2 μC are placed at (- 9, 0, 0) cm and (9, 0, 0) cm respectively in an external field E = \frac{A}{r ^{2}} r, where A = 9 \times 10^{5} N / C . m^{2} . Considering the potential at infinity is 0, the electrostatic energy of the configuration is____J.$ (1) $49.3$ (2) $-90.7$ (3) $24.3$ (4) $1.4$ 64. $Electric field in a region is given by E = Ax i + By j, where A = 10 V / m^{2} and B = 5 V / m^{2} . If the electric potential at a point (10, 20) is 500 V, then the electric potential at origin is____V.$ (1) $0$ (2) $2000$ (3) $500$ (4) $1000$ 65. $A charge 17.7 \times 10^{- 4} C is distributed uniformly over a large sheet of area 200 m^{2} . The electric intensity at a distance 20 cm from it in air will be (ϵ_{0} = 8.85 \times 10^{- 12} C^{2} / Nm^{2})$ (1) $5 \times 10^{5} N / C$ (2) $6 \times 10^{5} N / C$ (3) $7 \times 10^{5} N / C$ (4) $8 \times 10^{5} N / C$ 66. $The work done to move a charge on an equipotential surface is$ (1) $infinity$ (2) $less than 1$ (3) $greater than 1$ (4) $zero$ 67. $Three point charges 1 C, 2 C and 3C are placed at the corners of an equilateral triangle of side one meter. The work done to move these charges to the corners of another equilateral triangle of side 0.5 m is$ (1) $199 \times 10^{9} J$ (2) $19 \times 10^{9} J$ (3) $99 \times 10^{9} J$ (4) $29 \times 10^{9} J$ 68. $Given below are two statements: Statement-I: A point charge is brought in an electric field. The value of electric field at a point near to the charge may increase if the charge is positive Statement-II: An electric dipole is placed in a non-uniform electric field. The net electric force on the dipole will not be zero. Choose the correct answer from the options given below:$ (1) $Both statement-I and statement-II are true.$ (2) $Both statement-I and statement-I are false.$ (3) $Statement-I is true but statement-II is false.$ (4) $Statement-I is false but statement-II is true.$ 69. $An electron falls from rest through a vertical distance h in a uniform and vertically upward directed electric field E. The direction of electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest in it through the same vertical distance h. The time of fall of the electron, in comparison to the time of fall of the proton is$ (1) $smaller$ (2) $5 times greater$ (3) $10 times greater$ (4) $equal$ 70. $A point source of 100 W emits light with 5% efficiency. At a distance of 5 m from the source, the intensity produced by the electric field component is:$ (1) $\frac{1}{2 π} \frac{W}{m ^{2}}$ (2) $\frac{1}{40 π} \frac{W}{m ^{2}}$ (3) $\frac{1}{10 π} \frac{W}{m ^{2}}$ (4) $\frac{1}{20 π} \frac{W}{m ^{2}}$ 71. $If a capacitor of capacitance 100 μF is charged at a steady rate of 100 μC s^{- 1}, then the time taken to produce a potential difference of 100 V between the capacitor plates is$ (1) $50 s$ (2) $200 s$ (3) $150 s$ (4) $100 s$ 72. $For a uniformly charged ring of radius R, the electric field on its axis has the largest magnitude at a distance h from its center. Then value of h is:$ (1) $\frac{R}{5}$ (2) $\frac{R}{2}$ (3) $R$ (4) $R 2$ 73. $Two charges 7 μc and - 4 μc are placed at (- 7 cm, 0, 0) and (7 cm, 0, 0) respectively. Given, ϵ_{0} = 8.85 \times 10^{- 12} C^{2} N^{- 1} m^{- 2}, the electrostatic potential energy of the charge configuration is:$ (1) $-1.8 J$ (2) $-2.0 J$ (3) $-1.5 J$ (4) $-1.2 J$ 74. $A spherical shell of radius 10 cm is carrying a charge q. If the electric potential at distances 5 cm, 10 cm and 15 cm from the centre of the spherical shell is V_{1}, V_{2} and V_{3} respectively, then$ (1) $V_{1} < V_{2} < V_{3}$ (2) $V_{1} = V_{2} < V_{3}$ (3) $V_{1} > V_{2} > V_{3}$ (4) $V_{1} = V_{2} > V_{3}$ 75. $The electric field at a point on the equatorial plane at a distance r from the centre of a dipole having dipole moment P is given by (r ≫ separation of two charges forming the dipole, ϵ_{0} = permittivity of free space) [NEET 2020]$ (1) $E = \frac{p}{4 π ϵ _{0} r ^{3}}$ (2) $E = \frac{2 p}{4 π ϵ _{0} r ^{3}}$ (3) $E = - \frac{p}{4 π ϵ _{0} r ^{2}}$ (4) $E = - \frac{p}{4 π ϵ _{0} r ^{3}}$ 76. $Electric field due to infinite, straight uniformly charged wire varies with distance r as$ (1) $r$ (2) $\frac{1}{r}$ (3) $\frac{1}{r ^{2}}$ (4) $r^{2}$ 77. $The electric potential at any point x, y, z in metres is given by V = 3 x^{2} . The electric field at a point (2 m, 0, 1 m) is$ (1) $12 V m^{- 1}$ (2) $- 6 Vm^{- 1}$ (3) $6 V m^{- 1}$ (4) $- 12 Vm^{- 1}$ 78. $If E_{ax} and E_{eq} represents electric field at a point on the axial and equatorial line of a dipole. If points are at a distance r from the center of the dipole, for r ≫ a$ (1) $E_{ax} = E_{eq}$ (2) $E_{ax} = - E_{eq}$ (3) $E_{ax} = - 2 E_{eq}$ (4) $E_{eq} = 2 E_{ax}$ 79. $An electric dipole with dipole moment p is placed with its axis at 30^{\circ} to a uniform electric field. The work done in rotating the dipole to a position where its axis is perpendicular to the field is$ (1) $2pE$ (2) $\frac{2 pE}{3}$ (3) $\frac{3 pE}{2}$ (4) $0$ 80. $Two point charges A = + 3 nC and B = + 1 nC are placed 5 cm apart in air. The work done to move charge B towards A by 1 cm is$ (1) $2.0 \times 10^{- 7} J$ (2) $1.35 \times 10^{- 7} J$ (3) $2.7 \times 10^{- 7} J$ (4) $12.1 \times 10^{- 7} J$ 81. $A 2 gram object, located in a region of uniform electric field E = (300 N C^{- 1}) i carries a charge Q. The object released from rest at x = 0, has a kinetic energy of 0.12 J at x = 0.5 m . Then Q is$ (1) $400 μC$ (2) $- 400 μC$ (3) $800 μC$ (4) $- 800 μC$ 82. $An electric dipole of moment ´p´ is placed in an electric field of intensity ´E´. The dipole acquires a position such that the axis of the dipole makes an angle θ with the direction of the field. Assuming that the potential energy of the dipole to be zero when θ = 90º, the torque and the potential energy of the dipole will respectively be$ (1) $p E sinθ, - p E cosθ$ (2) $p E sinθ, - 2 p E cosθ$ (3) $p E sinθ, 2 p E cosθ$ (4) $p E cosθ, - p E cosθ$ 83. $There are three co-centric conducting spherical shells A, B and C of radii a, b and c respectively (c > b > a) and they are charged with charge q_{1}, q_{2} and q_{3} respectively. The potentials of the spheres A, B and C respectively, are :$ (1) $\frac{1}{4 π ϵ _{o}} (\frac{q _{1} + q _{2} + q _{3}}{a}), \frac{1}{4 π ϵ _{o}} (\frac{q _{1} + q _{2} + q _{3}}{b}), \frac{1}{4 π ϵ _{o}} (\frac{q _{1} + q _{2} + q _{3}}{c})$ (2) $\frac{1}{4 π ϵ _{o}} (\frac{q _{1}}{a} + \frac{q _{2}}{b} + \frac{q _{3}}{c}), \frac{1}{4 π ϵ _{o}} (\frac{q _{1} + q _{2} + q _{3}}{b}), \frac{1}{4 π ϵ _{o}} (\frac{q _{1} + q _{2} + q _{3}}{c})$ (3) $\frac{1}{4 π ϵ _{o}} (\frac{q _{1}}{a} + \frac{q _{2}}{b} + \frac{q _{3}}{c}), \frac{1}{4 π ϵ _{o}} (\frac{q _{1} + q _{2}}{b} + \frac{q _{3}}{c}), \frac{1}{4 π ϵ _{o}} (\frac{q _{1} + q _{2} + q _{3}}{c})$ (4) $\frac{1}{4 π ϵ _{o}} (\frac{q _{1} + q _{2} + q _{3}}{a}), \frac{1}{4 π ϵ _{o}} (\frac{q _{1} + q _{2}}{b} + \frac{q _{3}}{c}), \frac{1}{4 π ϵ _{o}} (\frac{q _{1}}{a} + \frac{q _{2}}{b} + \frac{q _{3}}{c})$ 84. $A small oil drop of mass 10^{- 6} kg is hanging in at rest between two plates separated by 1 mm having a potential difference of 500 V . The charge on the drop is (g = 10 m s^{- 2})$ (1) $2 \times 10^{- 9} C$ (2) $2 \times 10^{- 11} C$ (3) $2 \times 10^{- 6} C$ (4) $2 \times 10^{- 8} C$ 85. $Three charges + 2 q, + 3 q and - 4 q are situated at (0, - 3 a), (2 a, 0) and (- 2 a, 0) respectively in the xy plane. The resultant dipole moment about origin is____.$ (1) $2 qa (7 i - 3 j)$ (2) $2 qa (3 j - i)$ (3) $2 qa (3 i - 7 j)$ (4) $2 qa (3 j - 7 i)$ 86. $Two uniformly charged spherical conductors A and B of radii 5 mm and 10 mm are separated by a distance of 2 cm. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitudes of the electric fields at the surface of the sphere A and B will be:$ (1) $1 : 2$ (2) $2 : 1$ (3) $1 : 1$ (4) $1 : 4$ 87. $A spherical conductor of radius 10 cm has a charge of 3.2 \times 10^{- 7} C distributed uniformly. What is the magnitude of electric field at a point 15 cm from the center of the sphere? (\frac{1}{4 π ϵ _{0}} = 9 \times \frac{10 ^{9} Nm ^{2}}{C ^{2}}) [NEET 2020]$ (1) $1.28 \times 10^{5} N / C$ (2) $1.28 \times 10^{6} N / C$ (3) $1.28 \times 10^{7} N / C$ (4) $1.28 \times 10^{4} N / C$ 88. $The relative permittivity of distilled water is 81. The velocity of light in it will be: (Given μ_{r} = 1)$ (1) $4.33 \times 1 0^{7} m / s$ (2) $2.33 \times 1 0^{7} m / s$ (3) $3.33 \times 1 0^{7} m / s$ (4) $5.33 \times 1 0^{7} m / s$ 89. $The electric field in a region is given by E = \frac{2}{5} E_{0} i + \frac{3}{5} E_{0} j with E_{0} = 4.0 \times 10^{3} \frac{N}{C} . The flux of this field through a rectangular surface area 0.4 m^{2} parallel to the Y - Z plane is_______Nm^{2} C^{- 1}$ 90. $An electric dipole of dipole moment 6 \times 10^{- 6} Cm is placed in uniform electric field of magnitude 10^{6} V / m . Initially, the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field, will be J.$