Electrostatics PYQs Set 8 (PDF)

Set 8 of 13 · Questions 211-240 of 385

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Mere Teacher · Previous Year Questions JEE Main Physics · Electrostatics · Set 8 (Q211-240)
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211. $The charges Q, + q and +q are placed at the vertices of an equilateral triangle of side l. If the net electrostatic potential energy of the system is zero, the Q is equal to$ (1) $+ q /2$ (2) $zero$ (3) $- q /2$ (4) $-q$ 212. $A two point charges 4q and -q are fixed on the x axis at x = - \frac{d}{2} and x = \frac{d}{2} respectively. If a third point charge 'q' is taken from the origin to x = d along the semicircle as shown in the figure, the energy of the charge will$ (1) $Decrease by \frac{q ^{2}}{4 π ϵ _{0} d}$ (2) $Decrease by \frac{4 q ^{2}}{3 π ϵ _{0} d}$ (3) $Increase by \frac{2 q ^{2}}{3 π ϵ _{0} d}$ (4) $Increase by \frac{3 q ^{2}}{4 π ϵ _{0} d}$ 213. $A solid metal sphere of radius R having charge q is enclosed inside the concentric spherical shell of inner radius a and outer radius b as shown in figure. The approximate variation electric field E as a function of distance r from centre O is given by:$ (1) (2) (3) (4) 214. $A long cylindrical volume contains a uniformly distributed charge of density ρ. The radius of cylindrical volume is R. A charge particle (q) revolves around the cylinder in a circular path. The kinetic of the particle is:$ (1) $\frac{ρq R ^{2}}{4 ϵ _{0}}$ (2) $\frac{ρq R ^{2}}{2 ϵ _{0}}$ (3) $\frac{q ρ}{4 ϵ _{0} R ^{2}}$ (4) $\frac{4 ϵ _{0} R ^{2}}{q ρ}$ 215. $Two charges q and 3q are separated by a distance ' r ' in air. At a distance x from charge q, the resultant electric field is zero. The value of x is :$ (1) $\frac{( 1 + 3 )}{r}$ (2) $\frac{r}{3 ( 1 + 3 )}$ (3) $\frac{r}{( 1 + 3 )}$ (4) $r (1 + 3)$ 216. $Two identical metallic spheres A and B when placed at certain distance in air repel each other with a force of F. Another identical uncharged sphere C is first placed in contact with A and then in contact with B and finally placed at midpoint between spheres A and B. The force experienced by sphere C will be:$ (1) $3F/2$ (2) $3F/4$ (3) $F$ (4) $2F$ 217. $Four electric charges + q, + q, - q and -q are placed at the corners of a square of side 2L (see figure). The electric potential at point A, midway between the two charges +q and +q, is$ (1) $\frac{1}{4 π ϵ _{0}} \frac{2 q}{L} (1 + 5)$ (2) $\frac{1}{4 π ϵ _{0}} \frac{2 q}{L} (1 + \frac{1}{5})$ (3) $\frac{1}{4 π ϵ _{0}} \frac{2 q}{L} (1 - \frac{1}{5})$ (4) $zero$ 218. $Two spheres carrying charges + 6 μC and + 9 μC, separated by a distance d, experiences a force of repulsion F. When a charge of - 3 μC is given to both the sphere and kept at the same distance as before, the new force of repulsion is$ (1) $3F$ (2) $F /9$ (3) $F$ (4) $F /3$ 219. $Two charges of equal magnitude q are placed in air at a distance 2a apart and third charge -2q is placed at midpoint. The potential energy of the system is (ϵ_{0} = permittivity of free sapce)$ (1) $- \frac{q ^{2}}{8 π ϵ _{0} a}$ (2) $- \frac{3 q ^{2}}{8 π ϵ _{0} a}$ (3) $- \frac{5 q ^{2}}{8 π ϵ _{0} a}$ (4) $- \frac{7 q ^{2}}{8 π ϵ _{0} a}$ 220. $Two point charges q_{1} (10 μC) and q_{2} (- 25 μC) are placed on the x -axis at x = 1 m and x = 4 m respectively. The electric field (in V/m) at a point y = 3 m on y - axis is, (take \frac{1}{4 π \in _{0}} = 9 \times 10^{9} N m^{2} C^{- 2})$ (1) $(63 i - 27 j) \times 10^{2}$ (2) $(- 63 i + 27 j) \times 10^{2}$ (3) $(81 i - 81 j) \times 10^{2}$ (4) $(- 81 i - 81 j) \times 10^{2}$ 221. $Two isolated metallic solid spheres of radii R and 2R are charged such that both have same charge density σ. The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is σ'. The ratio \frac{σ ’}{σ} is:$ (1) $\frac{9}{4}$ (2) $\frac{4}{3}$ (3) $\frac{5}{3}$ (4) $\frac{5}{6}$ 222. $A hollow cylinder has a charge q coulomb within it. If ϕ is the electric flux in units of voltmeter associated with the curved surface B, the flux linked with the plane surface A in units of V‐m will be$ (1) $\frac{q}{2 ϵ _{0}}$ (2) $\frac{ϕ}{3}$ (3) $\frac{q}{ϵ _{0}} - φ$ (4) $\frac{1}{2} (\frac{q}{ϵ _{0}} - ϕ)$ 223. $A large charged plane having surface charge density 4.9 \times 10^{- 6} C m^{- 2} lies in the x - y plane. A circular plane of radius of 1 cm is lying completely in the region where x, y and z coordinates are all positive. When the plane's normal makes an angle 60^{\circ} with the z-axis, the electric flux through the circular plane is (\frac{1}{4 π ϵ _{0}} = 9 \times 10^{9} Nm^{2} C^{- 2})$ (1) $43.56 N m^{2} C^{- 1}$ (2) $48.36 N m^{2} C^{- 1}$ (3) $36.76 N m^{2} C^{- 1}$ (4) $32.56 N m^{2} C^{- 1}$ 224. $A solid sphere having radius R and Uniform charge density ρ has a cavity of radius R/2 as shown in figure. Find the ratio of magnitude of electric field at point A and B i.e. (\frac{E _{A}}{E _{B}}) .$ (1) $\frac{18}{19}$ (2) $\frac{11}{17}$ (3) $\frac{9}{17}$ (4) $\frac{9}{19}$ 225. $A metallic ring is uniformly charged as shown in figure. AC and BD are two mutually perpendicular diameters. Electric field due to arc AB at ' O ' is ' E ' in magnitude. What would be the magnitude of electric field at ' O ' due to arc ABC ?$ (1) $2E$ (2) $Zero$ (3) $E /2$ (4) $2 E$ 226. $Five positive charges each having charge q are placed at the vertices of a pentagon as shown in the figure. The electric potential (V) and the electric field (E) at the center O of the pentagon due to these five positive charges are:$ (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) $V = \frac{5 q}{4 π ϵ _{o} r} and E = \frac{5 q}{4 π ϵ _{o} r ^{2}} r$ 227. $Two infinite planes each with uniform surface charge density +σ are kept in such a way that the angle between them is 30^{\circ} . The electric field in the region shown between them is given by:$ (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) $\frac{σ}{2 ϵ _{0}} ((1 + \frac{3}{2}) y^+ \frac{1}{2} x^)$ 228. $The bob of a simple pendulum has mass 2 g and a charge of 5.0 μC . It is at rest in a uniform. It is at rest in a uniform horizontal electric field of intensity 2000V/m. At equilibrium, the angle that the pendulum makes with the vertical is: (take g = 10 m / s^{2})$ (1) $tan^{- 1} (2.0)$ (2) $tan^{- 1} (0.2)$ (3) $tan^{- 1} (5.0)$ (4) $tan^{- 1} (0.5)$ 229. $A charged cork ball having mass 1 g and charge q is suspended on a light string in a uniform electric field as shown in figure. The ball is in equilibrium at θ = 37^{\circ}, when value of electric field is E = (3 i + 5 j) \times 10^{5} NC^{- 1} . (Assume, T as tension in the string.) Which of the following options are correct? (Given, sin 37^{\circ} = 0.60 and g = 10 ms^{- 2}).$ (1) $q = 11 \times 10^{- 8} C$ (2) $T = 5.55 \times 10^{- 3} N$ (3) $q = 12 \times 10^{- 9} C$ (4) $T = 4.55 \times 10^{- 3} N$ 230. $A wire of length L has a charge Q distributed uniformly along its length. The wire is bent in the shape of a semicircle. The magnitude of the electric field at the center of curvature of the semicircle is$ (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) $\frac{1}{2 π ϵ _{0}} \frac{Q}{L ^{2}}$ 231. $A line charge of length \frac{a ^{’}}{2} is kept at the center of an edge BC of a cube ABCDEFGH having edge length 'a' as shown in the figure. If the density of line charge is λ C per unit length, then the total electric flux through all the faces of the cube will be (Take, ϵ_{0} as the free space permittivity)$ (1) $\frac{λa}{2 ϵ _{0}}$ (2) $\frac{λa}{4 ϵ _{0}}$ (3) $\frac{λa}{16 ϵ _{0}}$ (4) $\frac{λa}{8 ϵ _{0}}$ 232. $See the diagram. Area of each plate is 2.0 m^{2} and d = 2 \times 10^{- 3} m . A charge of 8.85 \times 10^{- 8} C is given to Q. Then the potential of Q becomes$ (1) $13 V$ (2) $10 V$ (3) $6.67 V$ (4) $8.825 V$ 233. $When a potential difference of 10^{3} V is applied between A and B, a charge of 0.75 mC is stored in the system of capacitors as shown. The value of C is (in μF)$ (1) $\frac{1}{2}$ (2) $2$ (3) $2.5$ (4) $3$ 234. $An infinitely long wire has uniform linear charge density λ = 2 nC / m . The net flux through a Gaussian cube of side length 3 cm, if the wire passes through any two corners of the cube, that are maximally displaced from each other, would be x Nm^{2} C^{- 1}, where x is: [Neglect any edge effects and use \frac{1}{4 π ϵ _{0}} = 9 \times 10^{9} SI units]$ (1) $6.48 π$ (2) $0.72 π$ (3) $1.44 π$ (4) $2.16 π$ 235. $The variation of electric potential with distance from a fixed point is shown in figure. What is the value of electric field at x = 2 m ?$ (1) $0$ (2) $3$ (3) $2$ (4) $6$ 236. $A point charge of 10µC is placed at the origin. At what location on the X-axis should a point charge of 40µC be placed so that the net electric field is zero at x = 2 cm on the X-axis?$ (1) $x = 6 cm$ (2) $x = 4cm$ (3) $x = 8cm$ (4) $x = -4cm$ 237. $Three concentric spherical metallic shells JC, Y and Z of radius a, b and c respectively [a < b < c] have surface charge densities σ, -σ and σ, respectively. The shells X and Z are at same potential. If the radii of X & Y are 2 cm and 3 cm, respectively. The radius of shell Z is_____cm.$ 238. $Suppose a uniformly charged wall provides a uniform electric field of 2 \times 10^{4} N / C normally. A charged particle of mass 2 g being suspended through a silk thread of length 20 cm and remain stayed at a distance of 10 cm from the wall. Then the charge on the particle will be \frac{1}{x} μC where x =______[use g = 10 m / s^{2}]$ 239. $A current of 6A enters one corner P of an equilateral triangle PQR having 3 wires of resistance 2Ω each and leaves by the corner R. The currents i_{i} in ampere is:$ 240. $Two identical charged spheres are suspended by string of equal lengths. The string make an angle of 37^{\circ} with each other. When suspended in a liquid of density 0.7 g / cm^{3}, the angle remains same. If density of material of the sphere is 1.4 g / cm^{3}, the dielectric constant of the liquid is______(tan 37^{\circ} = \frac{3}{4}) .$