Electrostatics PYQs Set 11 (PDF)

Set 11 of 13 · Questions 301-330 of 385

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Mere Teacher · Previous Year Questions JEE Main Physics · Electrostatics · Set 11 (Q301-330)
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301. $Two concentric spheres kept in air have radii R and r. They have similar charge and equal surface charge density σ. The electric potential at their common centre is (ϵ_{0} = permittivity of free space)$ (1) $\frac{σ ( R + r )}{ϵ _{0}}$ (2) $\frac{σ ( R - r )}{ϵ _{0}}$ (3) $\frac{σ ( R + r )}{2 ϵ _{0}}$ (4) $\frac{σ ( R + r )}{4 ϵ _{0}}$ 302. $A capacitor of capacitance 4 μF is charged to a potential difference of 6 V with a battery. The battery is removed and in its place another capacitor of capacitance is 8 μF introduced and the circuit is closed. The potential difference attained by each of the capacitors in V is$ (1) $2$ (2) $4$ (3) $6$ (4) $8$ 303. $The electric potential at the center of two concentric half rings of radii R_{1} and R_{2}, having same linear charge density λ, is$ (1) $\frac{2 λ}{\in _{0}}$ (2) $\frac{λ}{2 \in _{0}}$ (3) $\frac{λ}{4 \in _{0}}$ (4) $\frac{λ}{\in _{0}}$ 304. $A charge Q is situated at the corner of a cube, the electric flux passed through all the six faces of the cube is$ (1) $\frac{Q}{6 ϵ _{0}}$ (2) $\frac{Q}{8 ϵ _{0}}$ (3) $\frac{Q}{ϵ _{0}}$ (4) $\frac{Q}{2 ϵ _{0}}$ 305. $The figure shows three points A, B and C in a uniform electric field (E) . The line AB is perpendicular to BC and BC is parallel to E . If V_{A}, V_{B} and V_{C} are the potentials at A, B and C respectively, then the correct option is$ (1) $V_{A} = V_{B} = V_{C}$ (2) $V_{A} = V_{B} > V_{C}$ (3) $V_{A} = V_{B} < V_{C}$ (4) $V_{A} > V_{B} = V_{C}$ 306. $Two charges Q and 4Q are separated by a distance of 6 cm . The distance of the point from 4Q at which net electric field is zero is$ (1) $2 cm$ (2) $6 cm$ (3) $8 cm$ (4) $4 cm$ 307. $A semi-infinite non-conducting rod lies along X-axis with its left end at the origin. The rod has uniform linear charge density λ. The magnitude of electric field \| E \| at a point on the Y-axis at the distance L from the origin, will be$ (1) $\frac{λ}{4 π ϵ _{0} L}$ (2) $\frac{λ}{2 π ϵ _{0} L}$ (3) $\frac{λ}{2 2 π ϵ _{0} L}$ (4) $\frac{2 λ}{π ϵ _{0} L}$ 308. $The diagrams below show regions of equipotential A positive charge is moved from A to B in each diagram.$ (1) $In all the four cases the work done is the same.$ (2) $Minimum work is required to move q in figure (I).$ (3) $Maximum work is required to move q in figure (II).$ (4) $Maximum work is required to move q in figure (III).$ 309. $An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density σ_{0} . Choose the correct option from the following.$ (1) $Potential energy and torque both are maximum.$ (2) $Torque on dipole is zero and net force is directed away from the sheet.$ (3) $Torque on dipole is zero and net force acts towards the sheet.$ (4) $Potential energy of dipole is minimum and torque is zero.$ 310. $Two large plane parallel conducting plates are kept 10 cm apart as shown in figure. The potential difference between them is V. The potential difference between the points A and B (shown in the figure) is:$ (1) $1 V$ (2) $\frac{1}{4} V$ (3) $\frac{3}{4} V$ (4) $\frac{2}{5} V$ 311. $A uniform electric field vector E exists along horizontal direction as shown. The electric potential at A is V_{A} . A small point charge q is slowly taken from A to B along the curved path as shown. The potential energy of the charge when it is at point B is$ (1) $q (V_{A} - Ex)$ (2) $q (V_{A} + Ex)$ (3) $qEx -VA$ (4) $qEx$ 312. $Three charged particles A, B and C with charges - 4 q, 2 q and -2q are present on the circumference of a circle of radius d. The charged particles A, C and center P of the circle formed an equilateral triangle as shown in figure. Electric field at O along x -direction is:$ (1) $\frac{q}{4 π ϵ _{0} d ^{2}}$ (2) $\frac{q 3}{4 π ϵ _{0} d ^{2}}$ (3) $\frac{q 3}{π ϵ _{0} d ^{2}}$ (4) $\frac{q 3}{2 π ϵ _{0} d ^{2}}$ 313. $A small uncharged conducting sphere is placed in contact with an identical sphere but having 4 \times 10^{- 8} C charge and then removed to a distance such that the force of repulsion between them is 9 \times 10^{- 3} N . The distance between them is (Take \frac{1}{4 π ϵ _{0}} as 9 \times 10^{9} in SI units)$ (1) $3 cm$ (2) $2 cm$ (3) $4 cm$ (4) $1 cm$ 314. $Two electric dipoles, A, B with respective dipole moments d_{A} = - 4 qa i and d_{B} = - 2 qa i are placed on x -axis with a separation R, as shown in the figure The distance from A at which both of them produce the same potential is:$ (1) $\frac{R}{2 + 1}$ (2) $\frac{2 R}{2 + 1}$ (3) $\frac{R}{2 - 1}$ (4) $\frac{2 R}{2 - 1}$ 315. $What will be the magnitude of electric field at point O as shown in figure? Each side of the figure is l and perpendicular to each other?$ (1) $\frac{1}{4 π ϵ _{0}} \frac{q}{l ^{2}}$ (2) $\frac{1}{4 π ϵ _{0}} \frac{q}{( 2 l ^{2} )} (22 - 1)$ (3) $\frac{q}{4 π ϵ _{0} ( 2 l ^{2} )}$ (4) $\frac{1}{4 π ϵ _{0}} \frac{2 q}{( 2 l ^{2} )} (2)$ 316. $A point charge +q is placed at the origin. A second point charge + 9 q is placed at (d, 0, 0) in Cartesian coordinate system. The point in between them where the electric field vanishes is:$ (1) $(3 d /4, 0, 0)$ (2) $(d /4, 0, 0)$ (3) $(4 d /3, 0, 0)$ (4) $(d /3, 0, 0)$ 317. $Two identical capacitors C1 and C_{2} of equal capacitance are connected as shown in the circuit. Terminals a and b of the key k are connected to charge capacitor C1 using battery of emf V volt. Now, disconnecting a and b the terminals b and c are connected. Due to this, what will be the percentage loss of energy? [NEET 2019]$ (1) $75 %$ (2) $0 %$ (3) $50 %$ (4) $25 %$ 318. $Two electric charges + 2 μC and - 4 μC are separated by a distance 3 m in air. At a point P located on the line joining the two charges and in between them, the electric potential is zero. Then the electric field at a point P (in NC^{- 1}) is$ (1) $9,000$ (2) $18,000$ (3) $12,000$ (4) $27,000$ 319. $Two ideal electric dipoles A and B, having their dipole moment p_{1} and p_{2} respectively are placed on a plane with their centres at O as shown in the figure. At point C on the axis of dipole A, the resultant electric field is making an angle of 370 with the axis. The ratio of the dipole moment of A and B, \frac{p _{1}}{p _{2}} is: (take sin 3 7^{0} = \frac{3}{5})$ (1) $\frac{3}{8}$ (2) $\frac{3}{2}$ (3) $\frac{2}{3}$ (4) $\frac{4}{3}$ 320. $Two shorts dipoles (A, B), A having charges \pm 2 μC and length 1 cm and B having charges \pm 4 μC and length 1 cm are placed with their centres 80 cm apart as shown in the figure. The electric field at a point P, equi-distant from the centres of both dipoles is____N/C.$ (1) $\frac{9}{16} 2 \times 10^{4}$ (2) $92 \times 10^{4}$ (3) $4.5 2 \times 10^{4}$ (4) $\frac{9}{16} 2 \times 10^{5}$ 321. $Six point charges each of the magnitude Q are placed at the vertices of a regular hexagon of side a as shown in the figure. Electric field intensity on the line passing through the center O and perpendicular to the plane of the figure at a large distance x (>> a) from O is ( Let, (\frac{1}{4 π ϵ _{0}} = k)$ (1) $k \times \frac{4 Qa}{x ^{3}}$ (2) $k \times \frac{2 Qa}{x ^{3}}$ (3) $k \times \frac{8 Qa}{x ^{3}}$ (4) $0$ 322. $A charge Q is distributed over three concentric spherical shells of radii a, b, c (a < b < c) such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common centre, where r < a, would be$ (1) $\frac{Q}{12 π \in _{0}} \frac{ab + bc + ca}{abc}$ (2) $\frac{Q}{4 π \in _{0} ( a + b + c )}$ (3) $\frac{Q ( a + b + c )}{4 π \in _{0} ( a ^{2} + b ^{2} + c ^{2} )}$ (4) $\frac{Q ( a ^{2} + b ^{2} + c ^{2} )}{4 π \in _{0} ( a ^{3} + b ^{3} + c ^{3} )}$ 323. $A dipole is placed in an electric field as shown. In which direction will it move? [NEET 2021]$ (1) $Towards the left as its potential energy will increase$ (2) $Towards the right as its potential energy will decrease$ (3) $Towards the left as its potential energy will decrease$ (4) $Towards the right as its potential energy will increase$ 324. $σ is the uniform surface charge density of a thin spherical shell of radius R. The electric field at any point on the surface of the spherical shell is:$ (1) $σ / ϵ_{o} R$ (2) $σ / ϵ_{o}$ (3) $σ /4 ϵ_{o}$ (4) $σ /2 ϵ_{o}$ 325. $Two charges +q and -q, each 1 μC are arranged as shown in the figure. If x = 2 cm and y = 3 cm then potential difference (V_{A} - V_{B}) is$ (1) $5.4 \times 10^{2} V$ (2) $5.4 \times 10^{5} V$ (3) $5.2 \times 10^{2} V$ (4) $2.7 \times 10^{5} V$ 326. $How many 6 μF, 200 V condensers are needed to make a condenser of 18 μF, 600 V ?$ (1) $3$ (2) $27$ (3) $9$ (4) $18$ 327. $A point charge q = 1 μC is located at a distance 2 cm from one end of a thin insulating wire of length 10 cm having a charge Q = 24 μC, distributed uniformly along its length, as shown in figure. Force between q and wire is____N. (Use : \frac{1}{4 π ϵ _{o}} = 9 \times 10^{9} N . m^{2} / C^{2})$ 328. $As shown in the figure, a configuration of two equal point charges (q_{Q} = +2 µC) is placed on an inclined plane. Mass of each point charge is 20 g. Assume that there is no friction between charge and plane. For the system of two point charges to be in equilibrium (at rest) the height h = x x 10-3 m. The value of x is (Take \frac{1}{4 π ϵ _{0}} = 9 x 109 N m^{2} C^{- 2}, g = 10 m s^{- 2})$ 329. $A square loop of sides a = 1 m is held normally in front of a point charge q = 1 C . The flux of the electric field through the shaded region is \frac{5}{p} \times \frac{1}{ϵ _{0}} \frac{Nm ^{2}}{C}, where the value of p is .$ 330. $An electron revolves around an infinite cylindrical wire having uniform linear charge density 2 x 1 0^{- 8} C m^{- l} in circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of electron with which it is revolving is______________x 1 0^{6} m s^{- 1} . Given mass of electron = 9 x 1 0^{- 31} kg$