Electrostatics PYQs Set 10 (PDF)

Set 10 of 13 · Questions 271-300 of 385

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Mere Teacher · Previous Year Questions JEE Main Physics · Electrostatics · Set 10 (Q271-300)
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271. $A sphere encloses an electric dipole with charges \pm3 \times 1 0^{-6} C. What is the total electric flux across the sphere?$ (1) $- 3 \times 1 0^{-6}$ (2) $Zero$ (3) $3 \times 1 0^{-6} N m^{2} /C$ (4) $6 \times 1 0^{-6} N m^{2} /C$ 272. $A square surface of side L meter in the plane of the paper is placed in a uniform electric field E (volt / m) acting along the same plane at an angle Θ with the horizontal side of the square as shown in figure. The electric flux linked to the surface, in units of volt m is$ (1) $E L^{2}$ (2) $E L^{2} cos Θ$ (3) $E L^{2} sin Θ$ (4) $zero$ 273. $Two point charges A and B, having charges + Q and -Q respectively, are placed at certain distance apart and force acting between them is F. If 25% charge of A is transferred to B, then force between the charges becomes:$ (1) $\frac{4 F}{3}$ (2) $F$ (3) $\frac{9 F}{16}$ (4) $\frac{16 F}{9}$ 274. $Two charges 8 μC each are placed at the comers A and B of an equilateral triangle of side 0.2 m in air. The electric potential at the third comer C is$ (1) $7.2 \times 10^{5} V$ (2) $1.8 \times 10^{5} V$ (3) $3.6 \times 10^{5} V$ (4) $3.6 \times 10^{4} V$ 275. $Let σ be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electric fields in three different region E_{I}, E_{I I} and E_{I I I} are:$ (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) $E_{I} = - \frac{σ}{\in _{0}} n, E_{II} = 0, E_{III} = \frac{σ}{\in _{0}} n$ 276. $A charge Q is distributed over three concentric spherical shells of radii a, b, c (a < b < c) such that their surface charge densities are equal to one another. The total potential at a point at distance r from their common center, where r < a, would be:$ (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) $\frac{Q ( a + b + c )}{4 π \in _{0} ( a ^{2} + b ^{2} + c ^{2} )}$ 277. $Two electric dipoles, A, B with respective dipole moments d_{A} = - 4 qa i and d_{B} = - 2 qa i are placed on the x-axis with a separation R, as shown in the figure. The distance from A at which both of them produce the same potential is:$ (1) $\frac{R}{2 - 1}$ (2) $\frac{2 R}{2 + 1}$ (3) $\frac{2 R}{2 - 1}$ (4) $\frac{R}{2 + 1}$ 278. $C_{1} and C_{2} are two hollow concentric cubes enclosing charges 2Q and 3Q respectively as shown in figure. The ratio of electric flux passing through C_{1} and C_{2} is:$ (1) $2 : 5$ (2) $5 : 2$ (3) $2 : 3$ (4) $3 : 2$ 279. $For a short dipole placed at origin O, the dipole moment P is along x-axis, as shown in the figure. If the electric potential and electric field at A are V_{0} and E_{0}, respectively, then the correct combination of the electric potential and electric field, respectively, at point B on the y-axis is given by$ (1) $V_{0} and \frac{E _{0}}{4}$ (2) $zero and \frac{E _{0}}{16}$ (3) $zero and \frac{E _{0}}{8}$ (4) $\frac{V _{0}}{2} and \frac{E _{0}}{16}$ 280. $In the given circuit, if the potential difference between A and B is 80 V, then the equivalent capacitance between A and B and the charge on 10 μF capacitor respectively, are$ (1) $4μF and 133 μC$ (2) $164 μF and 150 μC$ (3) $15 μF and 200 μC$ (4) $4μF and 50 μC$ 281. $Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius R, with distance r from the center O is represented by:$ (1) (2) (3) (4) 282. $Two point charges -q and +q are placed at a distance of L, as shown in the figure. The magnitude of electric field intensity at a distance R (R ≫ L) varies as [NEET 2022]$ (1) $\frac{1}{R ^{3}}$ (2) $\frac{1}{R ^{4}}$ (3) $\frac{1}{R ^{6}}$ (4) $\frac{1}{R ^{2}}$ 283. $Six-point charges are kept 60^{\circ} apart from each other on the circumference of a circle of radius R as shown in figure. The net electric field at the center of the circle is____(ϵ_{0} is permittivity of free space)$ (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) $- \frac{Q}{4 π ϵ _{o} R ^{2}} (3 i - j)$ 284. $There is a uniform electric field of intensity E which is as shown. How many labelled points have the same electric potential as the fully shaded point?$ (1) $2$ (2) $3$ (3) $8$ (4) $11$ 285. $A hollow metal sphere of radius R is uniformly charged. The electric field due to the sphere at a distance r from the center [NEET 2019]$ (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) $increases as r increases for r < R and for r > R$ 286. $Two concentric spheres of radii R and r have positive charges q_{1} and q_{2} with equal surface charge densities. What is the electric potential at their common centre?$ (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) $\frac{σ}{ϵ _{0}} (\frac{R}{r})$ 287. $A uniformly charged disc of radius R having surface charge density σ is placed in the plane with its center at the origin. Find the electric field intensity along the z-axis at a Z distance from origin :-$ (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) $E = \frac{σ}{2 ϵ _{0}} (\frac{1}{( Z ^{2} + R ^{2} ) ^{1/2}} + \frac{1}{Z ^{2}})$ 288. $A point particle of charge Q is located at P along the axis of an electric dipole 1 at a distance r as shown in the figure. The point P is also on the equatorial plane of a second electric dipole 2 at a distance r. The dipoles are made of opposite charge q separated by a distance 2a. For the charge particle at P not to experience any net force, which of the following correctly describes the situation?$ (1) $\frac{a}{r} \sim 10$ (2) $\frac{a}{r} \sim 20$ (3) $\frac{a}{r} \sim 0.5$ (4) $\frac{a}{r} \sim 3$ 289. $Two charges q_{1} and q_{2} are separated by a distance of 30 cm. A third charge q3 initially at ' C ' as shown in the figure, is moved along the circular path of radius 40 cm from C to D. If the difference in potential energy due to movement of q3 from C to D is given by \frac{q _{3} K}{4 π ϵ _{0}}, the value of K is:$ (1) $6 q_{2}$ (2) $6 q_{1}$ (3) $8 q_{1}$ (4) $8 q_{2}$ 290. $The three charges q/2, q and q/2 are placed at the corners A, B and C of a square of side 'a' as shown in figure. The magnitude of electric field (E) at the comer D of the square, is:$ (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) $\frac{q}{4 π \in _{0} a ^{2}} (\frac{1}{2} - \frac{1}{2})$ 291. $Three point charges of + 2 q, + 2 q and -4q are placed at the corners A, B and C of an equilateral triangle ABC of side ' x ', The magnitude of the electric dipole moment of this system is$ (1) $23 q x$ (2) $2 q x$ (3) $3 q x$ (4) $32 q x$ 292. $A particle of mass 1 gm and charge 1 μC is held at rest on a frictionless horizontal surface at distance 1 m from the fixed charge 2 mC . If the particle is released, it will be repelled. The speed of the particle when it is at a distance of 10 m from the fixed charge is$ (1) $60 m s^{- 1}$ (2) $100 m s^{- 1}$ (3) $90 m s^{- 1}$ (4) $180 m s^{- 1}$ 293. $In a cuboid of dimension 2L \times 2L \times L, a charge q is placed at the center of the surface 'S' having area of 4 L^{2} . The flux through the opposite surface to 'S' is given by$ (1) $\frac{q}{12 ϵ _{0}}$ (2) $\frac{q}{3 ϵ _{0}}$ (3) $\frac{q}{2 ϵ _{0}}$ (4) $\frac{q}{6 ϵ _{0}}$ 294. $A, B and C are three points in a uniform electric field. The electric potential is:$ (1) $maximum at B$ (2) $maximum at C$ (3) $same at all the three points A, B and C$ (4) $maximum at A$ 295. $A small conducting sphere of radius r is lying concentrically inside a bigger hollow conducting sphere of radius R. The bigger and smaller spheres are charged with Q and q (Q > q) and are insulated from each other. The potential difference between the spheres will be$ (1) $\frac{1}{4 π ϵ _{0}} (\frac{q}{r} - \frac{Q}{R})$ (2) $\frac{1}{4 π ϵ _{0}} (\frac{Q}{R} + \frac{q}{r})$ (3) $\frac{1}{4 π ϵ _{0}} (\frac{q}{r} - \frac{q}{R})$ (4) $\frac{1}{4 π ϵ _{0}} (\frac{q}{R} - \frac{Q}{r})$ 296. $Two electric dipoles, each of dipole moment 'P' are placed at points A (a, 0) and B (- a, 0) as shown in the figure. The work done in rotating both the dipoles through 90^{\circ} in clockwise direction is (E = Electric field)$ (1) $PE$ (2) $Zero$ (3) $2PE$ (4) $\frac{PE}{2}$ 297. $Two infinite identical charged sheets and a charged spherical body of charge density ' ρ ' are arranged as shown in figure. Then the correct relation between the electrical fields at A, B, C and D points is:$ (1) $(E_{A}) = (E_{B}); E_{C} > E_{D}$ (2) $E_{A} = E_{B}; E_{C} = E_{D}$ (3) $E_{C} \neq = E_{D}; E_{A} > E_{B}$ (4) $E_{A} > E_{B}; E_{C} = E_{D}$ 298. $The distance between charges +q and -q is 2 l and between + 2 q and - 2 q is 4l. The electrostatic potential at point P at a distance r from centre O is - α (\frac{ql}{r ^{2}}) \times 10^{9} V, where the value of α is _____. (Use (\frac{1}{4 π ϵ _{0}} = 9 \times 10^{9} Nm^{2} C^{- 2})$ 299. $Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle θ with each other. When suspended in water the angle remains the same. If density of the material of the sphere is 1.5 g / cc, the dielectric constant of water will be______ (Take density of water = 1 g / cc)$ 300. $The electric field at point p due to an electric dipole is E. The electric field at point R on equitorial line will be \frac{E}{x} . The value of x:$