Electrostatics PYQs Set 9 (PDF)

Set 9 of 13 · Questions 241-270 of 385

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Mere Teacher · Previous Year Questions JEE Main Physics · Electrostatics · Set 9 (Q241-270)
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241. $Charges Q_{1} and Q_{2} are at points A and B of a right angle triangle OAB (see figure). The resultant electric field at point O is perpendicular to the hypotenuse, then Q_{1} / Q_{2} is proportional to$ (1) $\frac{x _{1}^{3}}{x _{2}^{3}}$ (2) $\frac{x _{2}^{2}}{x _{2}^{2}}$ (3) $\frac{x _{1}}{x _{2}}$ (4) $\frac{x _{2}}{x _{1}}$ 242. $Four point charges -Q, -q, 2q and 2Q are placed, one at each corner of the square. The relation between Q and q for which the potential at the centre of the square is zero is:$ (1) $Q = -q$ (2) $Q = - \frac{1}{q}$ (3) $Q = q$ (4) $Q = \frac{1}{q}$ 243. $An electric dipole is placed as shown in the figure. The electric potential (in 10^{2} V) at point P due to the dipole is (ϵ_{0} = permittivity of free space and \frac{1}{4 π ϵ _{0}} = K) [NEET 2023]$ (1) $(\frac{5}{8}) qK$ (2) $(\frac{8}{5}) qK$ (3) $(\frac{8}{3}) qK$ (4) $(\frac{3}{8}) qK$ 244. $A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field E . Due to the force q E, its velocity increases from 0 to 6 m/s in one second duration. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively$ (1) $2 m/s, 4 m/s$ (2) $1.5 m/s, 3 m/s$ (3) $1 m/s, 3.5 m/s$ (4) $1 m/s, 3 m/s$ 245. $An inclined plane making an angle 30^{\circ} with the horizontal is placed in a uniform horizontal electric field of 100 Vm^{- 1} as shown in the figure. A small block of mass 1 kg and charge, 0.01 C is allowed to slide down from rest from a height, h = 1 m . If the coefficient of friction is 0.2, then the acceleration of the block is nearly, (Acceleration due to gravity, g = 10 ms^{- 2})$ (1) $1.3 ms^{- 2}$ (2) $2.3 ms^{- 2}$ (3) $3.3 ms^{- 2}$ (4) $4.3 ms^{- 2}$ 246. $The equivalent capacitance between A and B in the given figure is$ (1) $\frac{2}{3} μF$ (2) $2 μF$ (3) $4 μF$ (4) $\frac{4}{3} μF$ 247. $Five charges + q, + 5 q, - 2 q, + 3 q and -4q are situated as shown in the figure. The electric flux due to this configuration through the surface S is:$ (1) $\frac{4 q}{ϵ _{0}}$ (2) $\frac{5 q}{ϵ _{0}}$ (3) $\frac{q}{ϵ _{0}}$ (4) $\frac{3 q}{ϵ _{0}}$ 248. $A point charge q is placed at the corner of a cube of side a as shown in the figure. What is the electric flux through the face ABCD ?$ (1) $\frac{q}{6 ϵ _{0}}$ (2) $\frac{q}{72 ϵ _{0}}$ (3) $0$ (4) $\frac{q}{24 ϵ _{0}}$ 249. $Concentric metallic hollow spheres of radii R and 4R hold charges Q_{1} and Q_{2} respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference V (R) - V (4 R) is$ (1) $\frac{3 Q _{2}}{4 π ϵ _{0} R}$ (2) $\frac{3 Q _{1}}{16 π ϵ _{0} R}$ (3) $\frac{Q _{2}}{4 π ϵ _{0} R}$ (4) $\frac{3 Q _{1}}{4 π ϵ _{0} R}$ 250. $Two point charges A and B of magnitude +8x 1 0^{- 6} C and -8x 1 0^{- 6} C respectively are placed at a distance d apart. The electric field at the middle point O between the charges is 6.4x104 NC-1. The distance 'd' between the point charges A and B is:$ (1) $2.0m$ (2) $3.0m$ (3) $1.0m$ (4) $4.0m$ 251. $Two charges each of charge + 10 μC are kept on Y-axis at y = - a and y = + a, respectively. Another point charge - 20 μC is placed at the origin and given a small displacement x (x << a) along X-axis. The force acting on the point charge is (x and a are in metres, \frac{1}{4 π ϵ _{0}} = 9 \times 10^{9} N - m^{2} C^{- 2})$ (1) $\frac{3.6 x}{a ^{2}} N$ (2) $\frac{2.4 x ^{2}}{a} N$ (3) $\frac{3.6 x}{a ^{3}} N$ (4) $\frac{4.8 x}{a ^{2}} N$ 252. $In this diagram, the P.D. between A and B is 60 V . The P.D. across 6 μF capacitor is ...V$ (1) $10$ (2) $5$ (3) $20$ (4) $4$ 253. $A square surface of side L meters is in the plane of the paper. A uniform electric field E (volt/m), also in the plane of the paper is limited only to the lower half of the square surface (see figure). The electric flux in SI units associated with the surface is$ (1) $E L^{2}$ (2) $E L^{2} /2 ϵ_{0}$ (3) $E L^{2} /2$ (4) $zero$ 254. $Three point charges + q, - 2 q and +q are placed at points (x = 0, y = a, z = 0), (x = 0, y = 0, z = 0) and (x = a, y = 0, z = 0) respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are$ (1) $2 qa along the line joining points x=0,y=0,z=0 and ( x=a,y=a,z=0)$ (2) $qa along the line joining points (x = 0, y = 0, z = 0) and (x = a, y = a, z = 0)$ (3) $2 qa along +x direction$ (4) $2 qa along +y direction.$ 255. $As per the diagram a point charge +q is placed at the origin O . Work done in taking another point charge -Q from the point A [coordinates (0, a)] to another point B [coordinates (a, 0)] along the straight path AB is$ (1) $zero$ (2) $(\frac{qQ}{4 π ϵ _{0}} \frac{1}{a ^{2}}) 2 a$ (3) $(\frac{- qQ}{4 π ϵ _{0}} \frac{1}{a ^{2}}) 2 a$ (4) $(\frac{qQ}{4 π ϵ _{0}} \frac{1}{a ^{2}}) \cdot \frac{a}{2}$ 256. $4 \times 10^{10} electrons are removed from a neutral metal sphere of diameter 20 cm placed in air. The magnitude of the electric field (in N C^{- 1}) at a distance of 20 cm from its centre is$ (1) $Zero$ (2) $5760$ (3) $640$ (4) $1440$ 257. $Four point charges - q, + q, + q and -q are placed on y-axis at y = - 2 d, y = - d, y = + 2 d, respectively. The magnitude of the electric field E at a point on the x -axis at x = D, with D ≫ d, will behave as:$ (1) $E \propto \frac{1}{D ^{3}}$ (2) $E \propto \frac{1}{D}$ (3) $E \propto \frac{1}{D ^{4}}$ (4) $E \propto \frac{1}{D ^{2}}$ 258. $Three charges are arranged on the vertices of a right angle triangle as shown in the figure. The magnitude of dipole moment of the combination in the unit of cm is$ (1) $102$ (2) $5$ (3) $103$ (4) $10$ 259. $The figure gives the electric potential V as a function of distance through four regions on x-axis. Which of the following is true for the magnitude of the electric field E in these regions?$ (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) $E_{A} = E_{C} and E_{B} < E_{D}$ 260. $The electric field at a point due to an electric dipole, on an axis inclined at an angle θ (< 90^{\circ}) to the dipole axis, is perpendicular to the dipole axis, if the angle θ is$ (1) $tan^{- 1} (2)$ (2) $tan^{- 1} (\frac{1}{2})$ (3) $tan^{- 1} (2)$ (4) $tan^{- 1} (\frac{1}{2})$ 261. $A simple pendulum of mass 'm', length 'l' and charge '+q' suspended in the electric field produced by two conducting parallel plates as shown. The value of deflection of pendulum in equilibrium position will be$ (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) $tan^{- 1} (\frac{q}{mg} \times \frac{C _{1} ( V _{1} + V _{2} )}{( C _{1} + C _{2} ) ( d - t )})$ 262. $A charge of 4µC is to be divided into two. The distance between the two divided charges is constant. The magnitude of the divided charges so that the force between them is maximum, will be:$ (1) $1µC and 3µC$ (2) $2µC and 2µC$ (3) $0 and 4µC$ (4) $1.5µC and 2.5µC$ 263. $Two charges q_{1} and q_{2} are placed 30 cm apart, as shown in the figure. A third charge q_{3} is moved along the arc of a circle of radius 40 cm from C to D . The change in the potential energy of the system is \frac{q _{3}}{4 π ϵ _{0}} k, where k is$ (1) $8 q_{1}$ (2) $6 q_{1}$ (3) $8 q_{2}$ (4) $6 q_{2}$ 264. $Find the electric field at point P (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length L carrying a charge Q. The distance of the point from the center of the rod is a = \frac{3}{2} L .$ (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) $\frac{Q}{4 π ϵ _{0} L ^{2}}$ 265. $Two identical parallel plate air capacitors are connected in series to a battery of e.m.f. V. If one of the capacitor is completely filled with dielectric material of constant K, then potential difference of the other capacitor will become$ (1) $\frac{K}{V ( K + 1 )}$ (2) $\frac{KV}{K + 1}$ (3) $\frac{K - 1}{KV}$ (4) $\frac{V}{K ( K + 1 )}$ 266. $Figure shows a rod AB, which is bent in a 12 0^{0} circular arc of radius R. A charge (- Q) is uniformly distributed over rod AB. What is the electric field E at the center of curvature O?$ (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) $\frac{3 3 Q}{8 π ^{2} ϵ _{0} R ^{2}} (- i)$ 267. $Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point P is \frac{xσ}{ϵ _{o}} . The value of x is______ (all quantities are measured in SI units).$ 268. $An electric field E \to= 4 x i^- (y^{2} + 1) j^N / C passes through the box shown in figure. The flux of the electric field through surface A B C D and B C GF and marked as φ_{I} and φ_{II} respectively. The difference between (φ_{I} - φ_{II}) is (in N m^{2} / C)$ 269. $If the net electric field at point P along Y axis is zero, then the ratio of (\frac{q _{2}}{q _{3}}) is \frac{8}{5 x}, where x =______$ 270. $An electric field E = (2 x i) N C^{- 1} exists in space. A cube of side 2 m is placed in the space as per figure given below. The electric flux through the cube is _______Nm^{2} / C .$