Electrostatics PYQs Set 7 (PDF)

Set 7 of 13 · Questions 181-210 of 385

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Mere Teacher · Previous Year Questions JEE Main Physics · Electrostatics · Set 7 (Q181-210)
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181. $The electric field in a region is given by E = (Ax + B) i, where E is in N C^{- 1} and x is in meters. The values of constants are A = 20 SI unit and B = 10 SI unit. If the potential at x = 1 is V_{1} and that at x = - 5 is V_{2} , then V_{1} - V_{2} is:-$ (1) $320 V$ (2) $-48V$ (3) $180 V$ (4) $-520 V$ 182. $A 60, μF parallel plate capacitor whose plates are separated by 6 mm is charged to 250 V, and then the charging source is removed. When a slab of dielectric constant 5 and thickness 3 mm is placed between the plates, find the change in the potential difference across the capacitor.$ (1) $250 V$ (2) $100 V$ (3) $150 V$ (4) $75 V$ 183. $Two identical charged particles each having a mass 10 g and charge 2.0 x 1 0^{- 7} C area placed on a horizontal table with a separation of L between then such that they stay in limited equilibrium. If the coefficient of friction between each particle and the table is 0.25, find the value of L. [Use g = 10 m s^{- 2}]$ (1) $12 cm$ (2) $10 cm$ (3) $8 cm$ (4) $5 cm$ 184. $A point charge of 10^{- 8} C is placed at origin. The work done in moving a point charge 2 μC from point A (4, 4, 2) m to B (2, 2, 1) m is____J. (\frac{1}{4 π ϵ _{o}} = 9 \times 10^{9}) in SI units)$ (1) $45 \times 10^{- 6}$ (2) $15 \times 10^{- 6}$ (3) $0$ (4) $30 \times 10^{- 6}$ 185. $A dipole of dipole moment p is placed in uniform electric field E then torque acting on it is given by$ (1) $τ = p \cdot E$ (2) $τ = p \times E$ (3) $τ = p + E$ (4) $τ = p - E$ 186. $An electric dipole has the magnitude of its charge as q and its dipole moment is p. It is placed in a uniform electric field E. If its dipole moment is along the direction of the field, the force on it and its potential energy are respectively$ (1) $2q . E and minimum$ (2) $q . E and p. E$ (3) $zero and minimum$ (4) $q . E and maximum$ 187. $Two identical electric point dipoles have dipole moments p_{1} \to= p i^and p_{2} \to= - p i^and are held on the x axis at distance 'a' from each other. When released, they move along the x-axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is 'm', their speed when they are infinitely far apart is$ (1) $\frac{p}{a} \frac{1}{2 π ϵ _{0} ma}$ (2) $\frac{p}{a} \frac{2}{π ϵ _{0} ma}$ (3) $\frac{p}{a} \frac{1}{π ϵ _{0} ma}$ (4) $\frac{p}{a} \frac{3}{2 π ϵ _{0} ma}$ 188. $Consider a circular loop that is uniformly charged and has a radius a 2 . Find the position along the positive z-axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in xy plane at the origin:$ (1) $a$ (2) $a /2$ (3) $0$ (4) $a / 2$ 189. $Given below are two statements: one is labelled a Assertion (A) and the other is labelled as Reason(R) Assertion (A): Work done by electric field on moving a positive charge on an equipotential surface is always zero. Reason (R): Electric lines of forces are always perpendicular to equipotential surfaces. In the light of the above statements, choose the most appropriate answer from the options given below:$ (1) $Both (A) and (R) are correct but (R) is not the correct explanation of (A)$ (2) $((A) is correct but (R) is not correct$ (3) $(A) is not correct but (R) is correct$ (4) $Both (A) and (R) are correct and (R) is the correct explanation of (A)$ 190. $Four equal point charges Q each are placed in the xy plane at (0, 2) (4, 2) (4, - 2) and (0, - 2) . The work required to put a fifth Q at the origin of the coordinate system will be:$ (1) $\frac{Q ^{2}}{4 π \in _{0}} (1 + \frac{1}{3})$ (2) $\frac{Q ^{2}}{4 π \in _{0}} (1 + \frac{1}{5})$ (3) $\frac{Q ^{2}}{2 2 π \in _{0}}$ (4) $\frac{Q ^{2}}{4 π \in _{0}}$ 191. $A point charge 2 x 1 0^{- 2} C is moved from P to S in a uniform electric field of 30 N C^{- 1} directed along positive x-axis. If coordinates of P and S are (1, 2, 0) m and (0, 0, 0) m respectively, the work done by electric field will be$ (1) $1200mJ$ (2) $600mJ$ (3) $-600mJ$ (4) $-l200mJ$ 192. $A cube of side L has point charges +q located at its seven vertices and -q at remsing one vertex. The electric field at its centre is found to be \| E \| = α (\frac{q}{4 π ϵ _{0} L ^{2}}) . The magnitude of constant α is$ (1) $\frac{4}{3}$ (2) $\frac{8}{3}$ (3) $3$ (4) $1$ 193. $In the situation shown in the diagram, magnitude of q << \| Q \| and r ≫ a . The net force on the free charge -q and net torque on it about O at the instant shown are respectively [p = 2 aQ is the dipole moment]$ (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) $\frac{1}{4 π ϵ _{0}} \frac{pq}{r ^{3}} i, + \frac{1}{4 π ϵ _{0}} \frac{pq}{r ^{2}} k$ 194. $Two charges of 5Q and -2Q are situated at the points (3 a, 0) and (- 5 a, 0) respectively. The electric flux through a sphere of radius ' 4a ' having center at origin is :$ (1) $\frac{2 Q}{ϵ _{0}}$ (2) $\frac{5 Q}{ϵ _{0}}$ (3) $\frac{7 Q}{ϵ _{0}}$ (4) $\frac{3 Q}{ϵ _{0}}$ 195. $Consider two infinitely large plane parallel conducting plates as shown below. The plates are uniformly charged with a surface charge density +σ and -2σ. The force experienced by a point charge +q placed at the mid point between two plates will be:$ (1) $\frac{3 σq}{4 ϵ _{0}}$ (2) $\frac{3 σq}{2 ϵ _{0}}$ (3) $\frac{σq}{4 ϵ _{0}}$ (4) $\frac{σq}{2 ϵ _{0}}$ 196. $The charge deposited on 4 μF capacitor in the circuit is$ (1) $6 \times 10^{- 6} C$ (2) $12 \times 10^{- 6} C$ (3) $24 \times 10^{- 6} C$ (4) $36\times 1 0^{- 6} C$ 197. $A solid conducting sphere, having a charge Q, is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given charge of - 4 Q, the new potential difference between the same two surfaces is:$ (1) $- 2 V$ (2) $2V$ (3) $4V$ (4) $V$ 198. $A thin non-conducting ring of radius r has a linear charge density λ = λ_{0} cos φ, where λ_{0} is a constant and φ is the azimuthal angle. The magnitude of the electric field strength at the centre of the ring is$ (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) $\frac{λ _{0}}{2 ϵ _{0} r}$ 199. $Charges Q are placed at the ends of a diagonal of a square and charges q are placed at the other two corners. The condition for the net electric force on Q to be zero is$ (1) $Q = - 22 q, q being negative$ (2) $Q = - \frac{q}{2}, q being negative$ (3) $Q = 22 q, q being negative$ (4) $Q = 2 q, q being negative$ 200. $Two point charges q_{1} (10 μC) and q_{2} (- 25 μC) are placed on the x-axis at x = 1 m and x = 4 m respectively. The electric field (in V/m) at a point y = 3 m on y-axis is, (k gS = \frac{1}{4 πg ϵ _{0}} = 9 \times 1 0^{9} N m^{2} C^{- 2})$ (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) $(63 i - 27 j) \times 1 0^{2}$ 201. $Two infinite planes each with uniform surface charge density +σ are kept in such a way that the angle between them is 30°. The electric field in the region shown between them is given by$ (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) $\frac{σ}{\in _{0}} ((1 + \frac{3}{2}) y + \frac{x}{2})$ 202. $A thin conducting ring of radius R is given a charge + Q. The electric field at the centre O of the ring due to the charge on the part AKB of the ring is E . The electric field at the center due to the charge on the part ACDB of the ring is$ (1) $E along KO$ (2) $3E along OK$ (3) $3E along KO$ (4) $E along OK$ 203. $In a parallel plate capacitor the separation between plates in 3x. This separation is filled by two layers of dielectrics, in which one layer has thickness x and dielectric constant 3k, the other layer is of thickness 2x and dielectric constant 5k, If the plates of the capacitor are connected to a battery, then the ratio of potential difference across the dielectric layers is$ (1) $\frac{1}{2}$ (2) $\frac{4}{3}$ (3) $\frac{3}{5}$ (4) $\frac{5}{6}$ 204. $Two identical conducting balls A and B have positive charges q_{1} and q_{2} respectively. But q_{1} \neq = q_{2} . The balls are brought together so that they touch each other and then kept in their original positions. The force between them is$ (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) $zero.$ 205. $A clock dial has point charges - q, - 2 q, - 3 q, \dots \dots \dots .. - 12 q at the positions of the corresponding numbers on the dial respectively. The time at which the hour's hand points the direction of the net electric field at the center of the dial is (Assume clock hands do not influence the net electric field)$ (1) $8 : 30$ (2) $9 : 30$ (3) $10 : 30$ (4) $12 : 30$ 206. $A cube of side 'a' has point charges +Q located at each of its vertices except at the origin where the charge is - Q. The electric field at the center of cube is:$ (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) $\frac{- Q}{3 3 π ϵ _{0} a ^{2}} (x + y + z)$ 207. $A circular wire loop of radius 10 cm carries a total charge of 10^{- 5} C distributed uniformly over its length. A small length of 3.14 \times 10^{- 6} m of wire is cut off. The magnitude to electric field at the center due to the remaining wire is (Assume, \frac{1}{4 π ϵ _{0}} = 9 \times 10^{9} SI units)$ (1) $30 N / C$ (2) $40 N / C$ (3) $35 N / C$ (4) $45 N / C$ 208. $The potential difference (V_{A} - V_{R}) in the arrangement shown in the figure is (q = 1 μC, x = 2 cm, y = 3 cm)$ (1) $5.4 \times 10^{5} V$ (2) $2.7 \times 10^{5} V$ (3) $5.4 \times 10^{2} V$ (4) $2.7 \times 10^{2} V$ 209. $Three point charges of magnitude 5 µC, 0.16 µC and 0.3 µC are located at the vertices A, B, C of a right angled triangle whose sides are AB = 3 cm, BC = 32 cm and CA = 3 cm and point A is the right angle corner. Charge at point A experiences _______ N of electrostatic force due to the other two charges.$ 210. $A long cylindrical volume contains a uniformly distributed charge of density ρC m^{- 3} . The electric field inside the cylindrical volume at a distance x = \frac{2 ϵ _{0}}{ρ} m from its axis is _____V m^{- 1}$