Electrostatics PYQs Set 8 (PDF)

Set 8 of 12 · Questions 211-240 of 349

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Mere Teacher · Previous Year Questions NEET Physics · Electrostatics · Set 8 (Q211-240)
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211. $A metallic ring is uniformly charged as shown in figure. AC and BD are two mutually perpendicular diameters. Electric field due to arc AB at ' O ' is ' E ' in magnitude. What would be the magnitude of electric field at ' O ' due to arc ABC ?$ (1) $2E$ (2) $Zero$ (3) $E /2$ (4) $2 E$ 212. $Five positive charges each having charge q are placed at the vertices of a pentagon as shown in the figure. The electric potential (V) and the electric field (E) at the center O of the pentagon due to these five positive charges are:$ (1) $V = \frac{5 q}{4 π ϵ _{o} r} and E = \frac{5 3 q}{8 π ϵ _{o} r ^{2}} r$ (2) $V = \frac{5 q}{4 π ϵ _{o} r} and E=0$ (3) $V = 0 and E=0$ (4) $V = \frac{5 q}{4 π ϵ _{o} r} and E = \frac{5 q}{4 π ϵ _{o} r ^{2}} r$ 213. $Two infinite planes each with uniform surface charge density +σ are kept in such a way that the angle between them is 30^{\circ} . The electric field in the region shown between them is given by:$ (1) $\frac{σ}{2 ϵ _{0}} ((1 - \frac{3}{2}) y^- \frac{1}{2} x^)$ (2) $\frac{σ}{2 ϵ _{0}} ((1 + \frac{3}{2}) y^- \frac{1}{2} x^)$ (3) $\frac{σ}{2 ϵ _{0}} ((1 - \frac{3}{2}) y^+ \frac{1}{2} x^)$ (4) $\frac{σ}{2 ϵ _{0}} ((1 + \frac{3}{2}) y^+ \frac{1}{2} x^)$ 214. $The bob of a simple pendulum has mass 2 g and a charge of 5.0 μC . It is at rest in a uniform. It is at rest in a uniform horizontal electric field of intensity 2000V/m. At equilibrium, the angle that the pendulum makes with the vertical is: (take g = 10 m / s^{2})$ (1) $tan^{- 1} (2.0)$ (2) $tan^{- 1} (0.2)$ (3) $tan^{- 1} (5.0)$ (4) $tan^{- 1} (0.5)$ 215. $A charged cork ball having mass 1 g and charge q is suspended on a light string in a uniform electric field as shown in figure. The ball is in equilibrium at θ = 37^{\circ}, when value of electric field is E = (3 i + 5 j) \times 10^{5} NC^{- 1} . (Assume, T as tension in the string.) Which of the following options are correct? (Given, sin 37^{\circ} = 0.60 and g = 10 ms^{- 2}).$ (1) $q = 11 \times 10^{- 8} C$ (2) $T = 5.55 \times 10^{- 3} N$ (3) $q = 12 \times 10^{- 9} C$ (4) $T = 4.55 \times 10^{- 3} N$ 216. $A wire of length L has a charge Q distributed uniformly along its length. The wire is bent in the shape of a semicircle. The magnitude of the electric field at the center of curvature of the semicircle is$ (1) $\frac{1}{4 π ϵ _{o}} \frac{Q}{L ^{2}}$ (2) $\frac{1}{4 π ϵ _{0}} \frac{Q ^{2}}{L}$ (3) $\frac{Q}{2 ϵ _{o}} \frac{1}{L ^{2}}$ (4) $\frac{1}{2 π ϵ _{0}} \frac{Q}{L ^{2}}$ 217. $A line charge of length \frac{a ^{’}}{2} is kept at the center of an edge BC of a cube ABCDEFGH having edge length 'a' as shown in the figure. If the density of line charge is λ C per unit length, then the total electric flux through all the faces of the cube will be (Take, ϵ_{0} as the free space permittivity)$ (1) $\frac{λa}{2 ϵ _{0}}$ (2) $\frac{λa}{4 ϵ _{0}}$ (3) $\frac{λa}{16 ϵ _{0}}$ (4) $\frac{λa}{8 ϵ _{0}}$ 218. $See the diagram. Area of each plate is 2.0 m^{2} and d = 2 \times 10^{- 3} m . A charge of 8.85 \times 10^{- 8} C is given to Q. Then the potential of Q becomes$ (1) $13 V$ (2) $10 V$ (3) $6.67 V$ (4) $8.825 V$ 219. $When a potential difference of 10^{3} V is applied between A and B, a charge of 0.75 mC is stored in the system of capacitors as shown. The value of C is (in μF)$ (1) $\frac{1}{2}$ (2) $2$ (3) $2.5$ (4) $3$ 220. $An infinitely long wire has uniform linear charge density λ = 2 nC / m . The net flux through a Gaussian cube of side length 3 cm, if the wire passes through any two corners of the cube, that are maximally displaced from each other, would be x Nm^{2} C^{- 1}, where x is: [Neglect any edge effects and use \frac{1}{4 π ϵ _{0}} = 9 \times 10^{9} SI units]$ (1) $6.48 π$ (2) $0.72 π$ (3) $1.44 π$ (4) $2.16 π$ 221. $The variation of electric potential with distance from a fixed point is shown in figure. What is the value of electric field at x = 2 m ?$ (1) $0$ (2) $3$ (3) $2$ (4) $6$ 222. $A point charge of 10µC is placed at the origin. At what location on the X-axis should a point charge of 40µC be placed so that the net electric field is zero at x = 2 cm on the X-axis?$ (1) $x = 6 cm$ (2) $x = 4cm$ (3) $x = 8cm$ (4) $x = -4cm$ 223. $Charges Q_{1} and Q_{2} are at points A and B of a right angle triangle OAB (see figure). The resultant electric field at point O is perpendicular to the hypotenuse, then Q_{1} / Q_{2} is proportional to$ (1) $\frac{x _{1}^{3}}{x _{2}^{3}}$ (2) $\frac{x _{2}^{2}}{x _{2}^{2}}$ (3) $\frac{x _{1}}{x _{2}}$ (4) $\frac{x _{2}}{x _{1}}$ 224. $Four point charges -Q, -q, 2q and 2Q are placed, one at each corner of the square. The relation between Q and q for which the potential at the centre of the square is zero is:$ (1) $Q = -q$ (2) $Q = - \frac{1}{q}$ (3) $Q = q$ (4) $Q = \frac{1}{q}$ 225. $An electric dipole is placed as shown in the figure. The electric potential (in 10^{2} V) at point P due to the dipole is (ϵ_{0} = permittivity of free space and \frac{1}{4 π ϵ _{0}} = K) [NEET 2023]$ (1) $(\frac{5}{8}) qK$ (2) $(\frac{8}{5}) qK$ (3) $(\frac{8}{3}) qK$ (4) $(\frac{3}{8}) qK$ 226. $A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field E . Due to the force q E, its velocity increases from 0 to 6 m/s in one second duration. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively$ (1) $2 m/s, 4 m/s$ (2) $1.5 m/s, 3 m/s$ (3) $1 m/s, 3.5 m/s$ (4) $1 m/s, 3 m/s$ 227. $An inclined plane making an angle 30^{\circ} with the horizontal is placed in a uniform horizontal electric field of 100 Vm^{- 1} as shown in the figure. A small block of mass 1 kg and charge, 0.01 C is allowed to slide down from rest from a height, h = 1 m . If the coefficient of friction is 0.2, then the acceleration of the block is nearly, (Acceleration due to gravity, g = 10 ms^{- 2})$ (1) $1.3 ms^{- 2}$ (2) $2.3 ms^{- 2}$ (3) $3.3 ms^{- 2}$ (4) $4.3 ms^{- 2}$ 228. $The equivalent capacitance between A and B in the given figure is$ (1) $\frac{2}{3} μF$ (2) $2 μF$ (3) $4 μF$ (4) $\frac{4}{3} μF$ 229. $Five charges + q, + 5 q, - 2 q, + 3 q and -4q are situated as shown in the figure. The electric flux due to this configuration through the surface S is:$ (1) $\frac{4 q}{ϵ _{0}}$ (2) $\frac{5 q}{ϵ _{0}}$ (3) $\frac{q}{ϵ _{0}}$ (4) $\frac{3 q}{ϵ _{0}}$ 230. $A point charge q is placed at the corner of a cube of side a as shown in the figure. What is the electric flux through the face ABCD ?$ (1) $\frac{q}{6 ϵ _{0}}$ (2) $\frac{q}{72 ϵ _{0}}$ (3) $0$ (4) $\frac{q}{24 ϵ _{0}}$ 231. $Concentric metallic hollow spheres of radii R and 4R hold charges Q_{1} and Q_{2} respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference V (R) - V (4 R) is$ (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) $\frac{3 Q _{1}}{4 π ϵ _{0} R}$ 232. $Two point charges A and B of magnitude +8x 1 0^{- 6} C and -8x 1 0^{- 6} C respectively are placed at a distance d apart. The electric field at the middle point O between the charges is 6.4x104 NC-1. The distance 'd' between the point charges A and B is:$ (1) $2.0m$ (2) $3.0m$ (3) $1.0m$ (4) $4.0m$ 233. $Two charges each of charge + 10 μC are kept on Y-axis at y = - a and y = + a, respectively. Another point charge - 20 μC is placed at the origin and given a small displacement x (x << a) along X-axis. The force acting on the point charge is (x and a are in metres, \frac{1}{4 π ϵ _{0}} = 9 \times 10^{9} N - m^{2} C^{- 2})$ (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) $\frac{4.8 x}{a ^{2}} N$ 234. $In this diagram, the P.D. between A and B is 60 V . The P.D. across 6 μF capacitor is ...V$ (1) $10$ (2) $5$ (3) $20$ (4) $4$ 235. $A square surface of side L meters is in the plane of the paper. A uniform electric field E (volt/m), also in the plane of the paper is limited only to the lower half of the square surface (see figure). The electric flux in SI units associated with the surface is$ (1) $E L^{2}$ (2) $E L^{2} /2 ϵ_{0}$ (3) $E L^{2} /2$ (4) $zero$ 236. $Three point charges + q, - 2 q and +q are placed at points (x = 0, y = a, z = 0), (x = 0, y = 0, z = 0) and (x = a, y = 0, z = 0) respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are$ (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) $2 qa along +y direction.$ 237. $As per the diagram a point charge +q is placed at the origin O . Work done in taking another point charge -Q from the point A [coordinates (0, a)] to another point B [coordinates (a, 0)] along the straight path AB is$ (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) $(\frac{qQ}{4 π ϵ _{0}} \frac{1}{a ^{2}}) \cdot \frac{a}{2}$ 238. $4 \times 10^{10} electrons are removed from a neutral metal sphere of diameter 20 cm placed in air. The magnitude of the electric field (in N C^{- 1}) at a distance of 20 cm from its centre is$ (1) $Zero$ (2) $5760$ (3) $640$ (4) $1440$ 239. $Four point charges - q, + q, + q and -q are placed on y-axis at y = - 2 d, y = - d, y = + 2 d, respectively. The magnitude of the electric field E at a point on the x -axis at x = D, with D ≫ d, will behave as:$ (1) $E \propto \frac{1}{D ^{3}}$ (2) $E \propto \frac{1}{D}$ (3) $E \propto \frac{1}{D ^{4}}$ (4) $E \propto \frac{1}{D ^{2}}$ 240. $Three charges are arranged on the vertices of a right angle triangle as shown in the figure. The magnitude of dipole moment of the combination in the unit of cm is$ (1) $102$ (2) $5$ (3) $103$ (4) $10$