Electrostatics PYQs Set 9 (PDF)

Set 9 of 12 · Questions 241-270 of 349

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Mere Teacher · Previous Year Questions NEET Physics · Electrostatics · Set 9 (Q241-270)
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241. $The figure gives the electric potential V as a function of distance through four regions on x-axis. Which of the following is true for the magnitude of the electric field E in these regions?$ (1) $E_{B} = E_{D} and E_{A} < E_{C}$ (2) $E_{A} > E_{B} > E_{C} > E_{D}$ (3) $E_{A} < E_{B} < E_{C} < E_{D}$ (4) $E_{A} = E_{C} and E_{B} < E_{D}$ 242. $The electric field at a point due to an electric dipole, on an axis inclined at an angle θ (< 90^{\circ}) to the dipole axis, is perpendicular to the dipole axis, if the angle θ is$ (1) $tan^{- 1} (2)$ (2) $tan^{- 1} (\frac{1}{2})$ (3) $tan^{- 1} (2)$ (4) $tan^{- 1} (\frac{1}{2})$ 243. $A simple pendulum of mass 'm', length 'l' and charge '+q' suspended in the electric field produced by two conducting parallel plates as shown. The value of deflection of pendulum in equilibrium position will be$ (1) $tan^{- 1} (\frac{q}{mg} \times \frac{C _{1} ( V _{2} - V _{1} )}{( C _{1} + C _{2} ) ( d - t )})$ (2) $tan^{- 1} (\frac{q}{mg} \times \frac{C _{2} ( V _{2} - V _{1} )}{( C _{1} + C _{2} ) ( d - t )})$ (3) $tan^{- 1} (\frac{q}{mg} \times \frac{C _{2} ( V _{1} + V _{2} )}{( C _{1} + C _{2} ) ( d - t )})$ (4) $tan^{- 1} (\frac{q}{mg} \times \frac{C _{1} ( V _{1} + V _{2} )}{( C _{1} + C _{2} ) ( d - t )})$ 244. $A charge of 4µC is to be divided into two. The distance between the two divided charges is constant. The magnitude of the divided charges so that the force between them is maximum, will be:$ (1) $1µC and 3µC$ (2) $2µC and 2µC$ (3) $0 and 4µC$ (4) $1.5µC and 2.5µC$ 245. $Two charges q_{1} and q_{2} are placed 30 cm apart, as shown in the figure. A third charge q_{3} is moved along the arc of a circle of radius 40 cm from C to D . The change in the potential energy of the system is \frac{q _{3}}{4 π ϵ _{0}} k, where k is$ (1) $8 q_{1}$ (2) $6 q_{1}$ (3) $8 q_{2}$ (4) $6 q_{2}$ 246. $Find the electric field at point P (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length L carrying a charge Q. The distance of the point from the center of the rod is a = \frac{3}{2} L .$ (1) $\frac{Q}{2 3 π ϵ _{0} L ^{2}}$ (2) $\frac{3 Q}{4 π ϵ _{0} L ^{2}}$ (3) $\frac{Q}{3 π ϵ _{0} L ^{2}}$ (4) $\frac{Q}{4 π ϵ _{0} L ^{2}}$ 247. $Two identical parallel plate air capacitors are connected in series to a battery of e.m.f. V. If one of the capacitor is completely filled with dielectric material of constant K, then potential difference of the other capacitor will become$ (1) $\frac{K}{V ( K + 1 )}$ (2) $\frac{KV}{K + 1}$ (3) $\frac{K - 1}{KV}$ (4) $\frac{V}{K ( K + 1 )}$ 248. $Figure shows a rod AB, which is bent in a 12 0^{0} circular arc of radius R. A charge (- Q) is uniformly distributed over rod AB. What is the electric field E at the center of curvature O?$ (1) $\frac{3 3 Q}{8 π ϵ _{0} R ^{2}} (i)$ (2) $\frac{3 3 Q}{8 π ^{2} ϵ _{0} R ^{2}} (i)$ (3) $\frac{3 3 Q}{16 π ^{2} ϵ _{0} R ^{2}} (i)$ (4) $\frac{3 3 Q}{8 π ^{2} ϵ _{0} R ^{2}} (- i)$ 249. $A sphere encloses an electric dipole with charges \pm3 \times 1 0^{-6} C. What is the total electric flux across the sphere?$ (1) $- 3 \times 1 0^{-6}$ (2) $Zero$ (3) $3 \times 1 0^{-6} N m^{2} /C$ (4) $6 \times 1 0^{-6} N m^{2} /C$ 250. $A square surface of side L meter in the plane of the paper is placed in a uniform electric field E (volt / m) acting along the same plane at an angle Θ with the horizontal side of the square as shown in figure. The electric flux linked to the surface, in units of volt m is$ (1) $E L^{2}$ (2) $E L^{2} cos Θ$ (3) $E L^{2} sin Θ$ (4) $zero$ 251. $Two point charges A and B, having charges + Q and -Q respectively, are placed at certain distance apart and force acting between them is F. If 25% charge of A is transferred to B, then force between the charges becomes:$ (1) $\frac{4 F}{3}$ (2) $F$ (3) $\frac{9 F}{16}$ (4) $\frac{16 F}{9}$ 252. $Two charges 8 μC each are placed at the comers A and B of an equilateral triangle of side 0.2 m in air. The electric potential at the third comer C is$ (1) $7.2 \times 10^{5} V$ (2) $1.8 \times 10^{5} V$ (3) $3.6 \times 10^{5} V$ (4) $3.6 \times 10^{4} V$ 253. $Let σ be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electric fields in three different region E_{I}, E_{I I} and E_{I I I} are:$ (1) $E_{I} = \frac{2 σ}{\in _{0}} n, E_{II} = 0, E_{III} = \frac{2 σ}{\in _{0}} n$ (2) $E_{I} = 0, E_{II} = \frac{σ}{\in _{0}} n, E_{III} = 0$ (3) $E_{I} = \frac{σ}{2 \in _{0}} n, E_{II} = 0, E_{III} = \frac{σ}{2 \in _{0}} n$ (4) $E_{I} = - \frac{σ}{\in _{0}} n, E_{II} = 0, E_{III} = \frac{σ}{\in _{0}} n$ 254. $A charge Q is distributed over three concentric spherical shells of radii a, b, c (a < b < c) such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common center, where r < a, would be:$ (1) $\frac{Q}{12 π \in _{0}} \frac{ab + bc + ca}{abc}$ (2) $\frac{Q ( a ^{2} + b ^{2} + c ^{2} )}{4 π \in _{0} ( a ^{3} + b ^{3} + c ^{3} )}$ (3) $\frac{Q}{4 π \in _{0} ( a + b + c )}$ (4) $\frac{Q ( a + b + c )}{4 π \in _{0} ( a ^{2} + b ^{2} + c ^{2} )}$ 255. $Two electric dipoles, A, B with respective dipole moments d_{A} = - 4 qa i and d_{B} = - 2 qa i are placed on the x-axis with a separation R, as shown in the figure. The distance from A at which both of them produce the same potential is:$ (1) $\frac{R}{2 - 1}$ (2) $\frac{2 R}{2 + 1}$ (3) $\frac{2 R}{2 - 1}$ (4) $\frac{R}{2 + 1}$ 256. $C_{1} and C_{2} are two hollow concentric cubes enclosing charges 2Q and 3Q respectively as shown in figure. The ratio of electric flux passing through C_{1} and C_{2} is:$ (1) $2 : 5$ (2) $5 : 2$ (3) $2 : 3$ (4) $3 : 2$ 257. $For a short dipole placed at origin O, the dipole moment P is along x-axis, as shown in the figure. If the electric potential and electric field at A are V_{0} and E_{0}, respectively, then the correct combination of the electric potential and electric field, respectively, at point B on the y-axis is given by$ (1) $V_{0} and \frac{E _{0}}{4}$ (2) $zero and \frac{E _{0}}{16}$ (3) $zero and \frac{E _{0}}{8}$ (4) $\frac{V _{0}}{2} and \frac{E _{0}}{16}$ 258. $In the given circuit, if the potential difference between A and B is 80 V, then the equivalent capacitance between A and B and the charge on 10 μF capacitor respectively, are$ (1) $4μF and 133 μC$ (2) $164 μF and 150 μC$ (3) $15 μF and 200 μC$ (4) $4μF and 50 μC$ 259. $Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius R, with distance r from the center O is represented by:$ (1) (2) (3) (4) 260. $Two point charges -q and +q are placed at a distance of L, as shown in the figure. The magnitude of electric field intensity at a distance R (R ≫ L) varies as [NEET 2022]$ (1) $\frac{1}{R ^{3}}$ (2) $\frac{1}{R ^{4}}$ (3) $\frac{1}{R ^{6}}$ (4) $\frac{1}{R ^{2}}$ 261. $Six-point charges are kept 60^{\circ} apart from each other on the circumference of a circle of radius R as shown in figure. The net electric field at the center of the circle is____(ϵ_{0} is permittivity of free space)$ (1) $\frac{Q}{4 π ϵ _{0} R ^{2}} (3 i - j)$ (2) $- \frac{5 Q}{8 π ϵ _{o} R ^{2}} (i + 3 j)$ (3) $- (\frac{5 Q}{8 π ϵ _{0} R ^{2}}) (i - 3 j)$ (4) $- \frac{Q}{4 π ϵ _{o} R ^{2}} (3 i - j)$ 262. $There is a uniform electric field of intensity E which is as shown. How many labelled points have the same electric potential as the fully shaded point?$ (1) $2$ (2) $3$ (3) $8$ (4) $11$ 263. $A hollow metal sphere of radius R is uniformly charged. The electric field due to the sphere at a distance r from the center [NEET 2019]$ (1) $zero as r increases for r < R, decreases as r increases for r > R$ (2) $zero as r increases for r < R, increases as r increases for r > R$ (3) $decreases as r increases for r < R and for r > R$ (4) $increases as r increases for r < R and for r > R$ 264. $Two concentric spheres of radii R and r have positive charges q_{1} and q_{2} with equal surface charge densities. What is the electric potential at their common centre?$ (1) $\frac{σ}{ϵ _{0}} (R + r)$ (2) $\frac{σ}{ϵ _{0}} (R - r)$ (3) $\frac{σ}{ϵ _{0}} (\frac{1}{R} + \frac{1}{r})$ (4) $\frac{σ}{ϵ _{0}} (\frac{R}{r})$ 265. $A uniformly charged disc of radius R having surface charge density σ is placed in the plane with its center at the origin. Find the electric field intensity along the z-axis at a Z distance from origin :-$ (1) $E = \frac{σ}{2 ϵ _{0}} (1 - \frac{Z}{( Z ^{2} + R ^{2} ) ^{\frac{1}{2}}})$ (2) $E = \frac{σ}{2 ϵ _{0}} (1 + \frac{Z}{( Z ^{2} + R ^{2} ) ^{\frac{1}{2}}})$ (3) $E = \frac{2 ϵ _{0}}{σ} (\frac{1}{( Z ^{2} + R ^{2} ) ^{1/2}} + Z)$ (4) $E = \frac{σ}{2 ϵ _{0}} (\frac{1}{( Z ^{2} + R ^{2} ) ^{1/2}} + \frac{1}{Z ^{2}})$ 266. $A point particle of charge Q is located at P along the axis of an electric dipole 1 at a distance r as shown in the figure. The point P is also on the equatorial plane of a second electric dipole 2 at a distance r. The dipoles are made of opposite charge q separated by a distance 2a. For the charge particle at P not to experience any net force, which of the following correctly describes the situation?$ (1) $\frac{a}{r} \sim 10$ (2) $\frac{a}{r} \sim 20$ (3) $\frac{a}{r} \sim 0.5$ (4) $\frac{a}{r} \sim 3$ 267. $Two charges q_{1} and q_{2} are separated by a distance of 30 cm. A third charge q3 initially at ' C ' as shown in the figure, is moved along the circular path of radius 40 cm from C to D. If the difference in potential energy due to movement of q3 from C to D is given by \frac{q _{3} K}{4 π ϵ _{0}}, the value of K is:$ (1) $6 q_{2}$ (2) $6 q_{1}$ (3) $8 q_{1}$ (4) $8 q_{2}$ 268. $The three charges q/2, q and q/2 are placed at the corners A, B and C of a square of side 'a' as shown in figure. The magnitude of electric field (E) at the comer D of the square, is:$ (1) $\frac{q}{4 π \in _{0} a ^{2}} (\frac{1}{2} + \frac{1}{2})$ (2) $\frac{q}{4 π \in _{0} a ^{2}} (1 + \frac{1}{2})$ (3) $\frac{q}{4 π \in _{0} a ^{2}} (1 - \frac{1}{2})$ (4) $\frac{q}{4 π \in _{0} a ^{2}} (\frac{1}{2} - \frac{1}{2})$ 269. $Three point charges of + 2 q, + 2 q and -4q are placed at the corners A, B and C of an equilateral triangle ABC of side ' x ', The magnitude of the electric dipole moment of this system is$ (1) $23 q x$ (2) $2 q x$ (3) $3 q x$ (4) $32 q x$ 270. $A particle of mass 1 gm and charge 1 μC is held at rest on a frictionless horizontal surface at distance 1 m from the fixed charge 2 mC . If the particle is released, it will be repelled. The speed of the particle when it is at a distance of 10 m from the fixed charge is$ (1) $60 m s^{- 1}$ (2) $100 m s^{- 1}$ (3) $90 m s^{- 1}$ (4) $180 m s^{- 1}$