Electrostatics PYQs Set 7 (PDF)

Set 7 of 12 · Questions 181-210 of 349

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Mere Teacher · Previous Year Questions NEET Physics · Electrostatics · Set 7 (Q181-210)
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181. $In the situation shown in the diagram, magnitude of q << \| Q \| and r ≫ a . The net force on the free charge -q and net torque on it about O at the instant shown are respectively [p = 2 aQ is the dipole moment]$ (1) $\frac{1}{4 π ϵ _{0}} \frac{pq}{r ^{3}} i, - \frac{1}{4 π ϵ _{0}} \frac{pq}{r ^{2}} k$ (2) $\frac{1}{4 π ϵ _{0}} \frac{pq}{r ^{2}} k, \frac{1}{4 π ϵ _{0}} \frac{pq}{r ^{3}} i$ (3) $- \frac{1}{4 π ϵ _{0}} \frac{pq}{r ^{2}} k, - \frac{1}{4 π ϵ _{0}} \frac{pq}{r ^{3}} i$ (4) $\frac{1}{4 π ϵ _{0}} \frac{pq}{r ^{3}} i, + \frac{1}{4 π ϵ _{0}} \frac{pq}{r ^{2}} k$ 182. $Two charges of 5Q and -2Q are situated at the points (3 a, 0) and (- 5 a, 0) respectively. The electric flux through a sphere of radius ' 4a ' having center at origin is :$ (1) $\frac{2 Q}{ϵ _{0}}$ (2) $\frac{5 Q}{ϵ _{0}}$ (3) $\frac{7 Q}{ϵ _{0}}$ (4) $\frac{3 Q}{ϵ _{0}}$ 183. $Consider two infinitely large plane parallel conducting plates as shown below. The plates are uniformly charged with a surface charge density +σ and -2σ. The force experienced by a point charge +q placed at the mid point between two plates will be:$ (1) $\frac{3 σq}{4 ϵ _{0}}$ (2) $\frac{3 σq}{2 ϵ _{0}}$ (3) $\frac{σq}{4 ϵ _{0}}$ (4) $\frac{σq}{2 ϵ _{0}}$ 184. $The charge deposited on 4 μF capacitor in the circuit is$ (1) $6 \times 10^{- 6} C$ (2) $12 \times 10^{- 6} C$ (3) $24 \times 10^{- 6} C$ (4) $36\times 1 0^{- 6} C$ 185. $A solid conducting sphere, having a charge Q, is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given charge of - 4 Q, the new potential difference between the same two surfaces is:$ (1) $- 2 V$ (2) $2V$ (3) $4V$ (4) $V$ 186. $A thin non-conducting ring of radius r has a linear charge density λ = λ_{0} cos φ, where λ_{0} is a constant and φ is the azimuthal angle. The magnitude of the electric field strength at the centre of the ring is$ (1) $\frac{1}{4 π ϵ _{0}} \frac{λ _{0}}{r}$ (2) $\frac{1}{2 π ϵ _{0}} \frac{λ _{0}}{r}$ (3) $\frac{λ _{0}}{4 ϵ _{0} r}$ (4) $\frac{λ _{0}}{2 ϵ _{0} r}$ 187. $Charges Q are placed at the ends of a diagonal of a square and charges q are placed at the other two corners. The condition for the net electric force on Q to be zero is$ (1) $Q = - 22 q, q being negative$ (2) $Q = - \frac{q}{2}, q being negative$ (3) $Q = 22 q, q being negative$ (4) $Q = 2 q, q being negative$ 188. $Two point charges q_{1} (10 μC) and q_{2} (- 25 μC) are placed on the x-axis at x = 1 m and x = 4 m respectively. The electric field (in V/m) at a point y = 3 m on y-axis is, (k gS = \frac{1}{4 πg ϵ _{0}} = 9 \times 1 0^{9} N m^{2} C^{- 2})$ (1) $(- 81 i + 81 j) \times 1 0^{2}$ (2) $(81 i - 81 j) \times 1 0^{2}$ (3) $(- 63 i + 27 j) \times 1 0^{2}$ (4) $(63 i - 27 j) \times 1 0^{2}$ 189. $Two infinite planes each with uniform surface charge density +σ are kept in such a way that the angle between them is 30°. The electric field in the region shown between them is given by$ (1) $\frac{σ}{2 \in _{0}} ((1 + 3) y - \frac{x}{2})$ (2) $\frac{σ}{2 \in _{0}} ((1 - \frac{3}{2}) y - \frac{x}{2})$ (3) $\frac{σ}{2 \in _{0}} ((1 + 3) y + \frac{x}{2})$ (4) $\frac{σ}{\in _{0}} ((1 + \frac{3}{2}) y + \frac{x}{2})$ 190. $A thin conducting ring of radius R is given a charge + Q. The electric field at the centre O of the ring due to the charge on the part AKB of the ring is E . The electric field at the center due to the charge on the part ACDB of the ring is$ (1) $E along KO$ (2) $3E along OK$ (3) $3E along KO$ (4) $E along OK$ 191. $In a parallel plate capacitor the separation between plates in 3x. This separation is filled by two layers of dielectrics, in which one layer has thickness x and dielectric constant 3k, the other layer is of thickness 2x and dielectric constant 5k, If the plates of the capacitor are connected to a battery, then the ratio of potential difference across the dielectric layers is$ (1) $\frac{1}{2}$ (2) $\frac{4}{3}$ (3) $\frac{3}{5}$ (4) $\frac{5}{6}$ 192. $Two identical conducting balls A and B have positive charges q_{1} and q_{2} respectively. But q_{1} \neq = q_{2} . The balls are brought together so that they touch each other and then kept in their original positions. The force between them is$ (1) $less than that before the balls touched$ (2) $greater than that before the balls touched$ (3) $same as that before the balls touched$ (4) $zero.$ 193. $A clock dial has point charges - q, - 2 q, - 3 q, \dots \dots \dots .. - 12 q at the positions of the corresponding numbers on the dial respectively. The time at which the hour's hand points the direction of the net electric field at the center of the dial is (Assume clock hands do not influence the net electric field)$ (1) $8 : 30$ (2) $9 : 30$ (3) $10 : 30$ (4) $12 : 30$ 194. $A cube of side 'a' has point charges +Q located at each of its vertices except at the origin where the charge is - Q. The electric field at the center of cube is:$ (1) $\frac{2 Q}{3 3 π ϵ _{0} a ^{2}} (x + y + z)$ (2) $\frac{Q}{3 3 π ϵ _{0} a ^{2}} (x + y + z)$ (3) $\frac{- 2 Q}{3 3 π ϵ _{0} a ^{2}} (x + y + z)$ (4) $\frac{- Q}{3 3 π ϵ _{0} a ^{2}} (x + y + z)$ 195. $A circular wire loop of radius 10 cm carries a total charge of 10^{- 5} C distributed uniformly over its length. A small length of 3.14 \times 10^{- 6} m of wire is cut off. The magnitude to electric field at the center due to the remaining wire is (Assume, \frac{1}{4 π ϵ _{0}} = 9 \times 10^{9} SI units)$ (1) $30 N / C$ (2) $40 N / C$ (3) $35 N / C$ (4) $45 N / C$ 196. $The potential difference (V_{A} - V_{R}) in the arrangement shown in the figure is (q = 1 μC, x = 2 cm, y = 3 cm)$ (1) $5.4 \times 10^{5} V$ (2) $2.7 \times 10^{5} V$ (3) $5.4 \times 10^{2} V$ (4) $2.7 \times 10^{2} V$ 197. $The charges Q, + q and +q are placed at the vertices of an equilateral triangle of side l. If the net electrostatic potential energy of the system is zero, the Q is equal to$ (1) $+ q /2$ (2) $zero$ (3) $- q /2$ (4) $-q$ 198. $A two point charges 4q and -q are fixed on the x axis at x = - \frac{d}{2} and x = \frac{d}{2} respectively. If a third point charge 'q' is taken from the origin to x = d along the semicircle as shown in the figure, the energy of the charge will$ (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) $Increase by \frac{3 q ^{2}}{4 π ϵ _{0} d}$ 199. $A solid metal sphere of radius R having charge q is enclosed inside the concentric spherical shell of inner radius a and outer radius b as shown in figure. The approximate variation electric field E as a function of distance r from centre O is given by:$ (1) (2) (3) (4) 200. $A long cylindrical volume contains a uniformly distributed charge of density ρ. The radius of cylindrical volume is R. A charge particle (q) revolves around the cylinder in a circular path. The kinetic of the particle is:$ (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) $\frac{4 ϵ _{0} R ^{2}}{q ρ}$ 201. $Two charges q and 3q are separated by a distance ' r ' in air. At a distance x from charge q, the resultant electric field is zero. The value of x is :$ (1) $\frac{( 1 + 3 )}{r}$ (2) $\frac{r}{3 ( 1 + 3 )}$ (3) $\frac{r}{( 1 + 3 )}$ (4) $r (1 + 3)$ 202. $Two identical metallic spheres A and B when placed at certain distance in air repel each other with a force of F. Another identical uncharged sphere C is first placed in contact with A and then in contact with B and finally placed at midpoint between spheres A and B. The force experienced by sphere C will be:$ (1) $3F/2$ (2) $3F/4$ (3) $F$ (4) $2F$ 203. $Four electric charges + q, + q, - q and -q are placed at the corners of a square of side 2L (see figure). The electric potential at point A, midway between the two charges +q and +q, is$ (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) $zero$ 204. $Two spheres carrying charges + 6 μC and + 9 μC, separated by a distance d, experiences a force of repulsion F. When a charge of - 3 μC is given to both the sphere and kept at the same distance as before, the new force of repulsion is$ (1) $3F$ (2) $F /9$ (3) $F$ (4) $F /3$ 205. $Two charges of equal magnitude q are placed in air at a distance 2a apart and third charge -2q is placed at midpoint. The potential energy of the system is (ϵ_{0} = permittivity of free sapce)$ (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) $- \frac{7 q ^{2}}{8 π ϵ _{0} a}$ 206. $Two point charges q_{1} (10 μC) and q_{2} (- 25 μC) are placed on the x -axis at x = 1 m and x = 4 m respectively. The electric field (in V/m) at a point y = 3 m on y - axis is, (take \frac{1}{4 π \in _{0}} = 9 \times 10^{9} N m^{2} C^{- 2})$ (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) $(- 81 i - 81 j) \times 10^{2}$ 207. $Two isolated metallic solid spheres of radii R and 2R are charged such that both have same charge density σ. The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is σ'. The ratio \frac{σ ’}{σ} is:$ (1) $\frac{9}{4}$ (2) $\frac{4}{3}$ (3) $\frac{5}{3}$ (4) $\frac{5}{6}$ 208. $A hollow cylinder has a charge q coulomb within it. If ϕ is the electric flux in units of voltmeter associated with the curved surface B, the flux linked with the plane surface A in units of V‐m will be$ (1) $\frac{q}{2 ϵ _{0}}$ (2) $\frac{ϕ}{3}$ (3) $\frac{q}{ϵ _{0}} - φ$ (4) $\frac{1}{2} (\frac{q}{ϵ _{0}} - ϕ)$ 209. $A large charged plane having surface charge density 4.9 \times 10^{- 6} C m^{- 2} lies in the x - y plane. A circular plane of radius of 1 cm is lying completely in the region where x, y and z coordinates are all positive. When the plane's normal makes an angle 60^{\circ} with the z-axis, the electric flux through the circular plane is (\frac{1}{4 π ϵ _{0}} = 9 \times 10^{9} Nm^{2} C^{- 2})$ (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) $32.56 N m^{2} C^{- 1}$ 210. $A solid sphere having radius R and Uniform charge density ρ has a cavity of radius R/2 as shown in figure. Find the ratio of magnitude of electric field at point A and B i.e. (\frac{E _{A}}{E _{B}}) .$ (1) $\frac{18}{19}$ (2) $\frac{11}{17}$ (3) $\frac{9}{17}$ (4) $\frac{9}{19}$