Electrostatics PYQs Set 6 (PDF)

Set 6 of 13 · Questions 151-180 of 385

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Mere Teacher · Previous Year Questions JEE Main Physics · Electrostatics · Set 6 (Q151-180)
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151. $An electric dipole with dipole moment 4 \times 10^{- 9} Cm is aligned at 30^{\circ} with the direction of a uniform electric field of magnitude 5 \times 10^{4} N C^{- 1}, the magnitude of the torque acting on the dipole is$ (1) $10^{- 5} N m$ (2) $10^{- 4} N m$ (3) $10 \times 10^{- 3} N m$ (4) $3\times 10^{- 4} N m$ 152. $An electric dipole of moment p = (- i^- 3 j^+ 2 k^) \times 1 0^{- 29} C.m. is at the origin (0, 0, 0). The electric field due to this dipole at r = (+ i^+ 3 j^+ 5 k^) (note that r . p = 0) is parallel to :$ (1) $(+ i^+ 3 j^- 2 k^)$ (2) $(- i^+ 3 j^- 2 k^)$ (3) $(+ i^- 3 j^- 2 k^)$ (4) $(- i^- 3 j^+ 2 k^)$ 153. $An electric dipole of moment p is placed in an electric field of intensity E. The dipole acquires a position such that the axis of the dipole makes an angle 6 with the direction of the field. Assuming that the potential energy of the dipole to be zero when Θ = 9 0^{o}, the torque and the potential energy of the dipole will respectively be$ (1) $pE sin Θ,-pE cos Θ$ (2) $pE sin Θ,-2pE cos Θ$ (3) $pE sin Θ,2pE cos Θ$ (4) $pE cos Θ,-pE sin Θ$ 154. $A charged cylinder of radius 3 mm has surface charge density 4 μC / m^{2} . It is placed in a medium of dielectric constant 628. The electric intensity at a point at a distance of 1.5 m from its axis is$ (1) $1.44 V / m$ (2) $2.44 V / m$ (3) $3 V / m$ (4) $0.5 V / m$ 155. $An electric dipole is placed at an angle of 30º with an electric field intensity 2 \times 1 0^{5} N/C. It experiences a torque equal to 4 N m. The charge on the dipole, if the dipole length is 2cm, is$ (1) $7 µC$ (2) $8 mC$ (3) $2 mC$ (4) $5 mC$ 156. $An electrician requires a capacitance of 6 μF in a circuit across a potential difference of 1.5 kV . A large number of 2 μF capacitors which can withstand a potential difference of not more than 500 V are available. The minimum number of capacitors required for the purpose is$ (1) $3$ (2) $9$ (3) $6$ (4) $27$ 157. $The minimum work needed to be done to bring a charge q = 6 μC from \infty to a point 0.75 m from a charge Q = 30 μC is$ (1) $4.16 J$ (2) $5.16 J$ (3) $2.16 J$ (4) $1.16 J$ 158. $A region contains a uniform electric field E = (10 i + 30 j) Vm^{- 1} \cdot A and B are two points in the field at (1, 2, 0) m and (2, 1, 3) m, respectively. The work done when a charge of 0.8 C moves from A to B in a parabolic path is$ (1) $8 J$ (2) $80 J$ (3) $40 J$ (4) $16 J$ 159. $An electric dipole is placed at an angle of 30 ° with an electric field intensity 2 \times 1 0^{5} N C^{- 1} . It experiences a torque equal to 4 Nm . The charge on the dipole, if the dipole length is 2 cm, is$ (1) $8 mC$ (2) $2 mC$ (3) $5 mC$ (4) $7 μC$ 160. $The vehicles carrying inflammable fluids usually have metallic chains touching the ground:$ (1) $To protect tyres from catching dirt from ground$ (2) $To alert other vehicles$ (3) $It is a custom$ (4) $To conduct excess charge due to air friction to ground and prevent sparking$ 161. $A bullet of mass 2g is having a charge of 2 μC . Through what potential difference must it be accelerated, starting from rest, to acquire a speed of10 m/s 7.$ (1) $5kV$ (2) $50kV$ (3) $5V$ (4) $50V$ 162. $At what temperature a gold ring of diameter 6.230 cm be heated so that it can be fitted on a wooden bangle of diameter 6.241 cm? Both the diameters have been measured at room temperature (27°C). (Given: coefficient of linear thermal expansion of gold α_{L} = 1.4 \times 1 0^{- 5} K^{- 1})$ (1) $125.7°C$ (2) $91.7°C$ (3) $425.7°$ (4) $152.7°C$ 163. $A particle of charge ' -q ' and mass ' m' moves in a circle of radius ' r ' around an infinitely long line charge of linear density ' +λ '. Then time period will be given as: (Consider k as Coulomb's constant)$ (1) $T^{2} = \frac{4 π ^{2} m}{2 kλq} r^{3}$ (2) $T = 2 πr \frac{m}{2 kλq}$ (3) $T = \frac{1}{2 πr} \frac{m}{2 kλq}$ (4) $T = \frac{1}{2 π} \frac{2 kλq}{m}$ 164. $Some charge is being given to a conductor. Then its potential is$ (1) $maximum at surface$ (2) $maximum at center$ (3) $remain same throughout the conductor$ (4) $maximum somewhere between surface and center.$ 165. $An α-particle of mass 6.4 \times 10^{- 27} kg and charge 3.2 \times 10^{- 19} C is situated in a uniform electric field of 1.6 \times 10^{5} V m^{- 1} . The velocity of the particle at the end of 2 \times 10^{- 2} m path when it starts from rest is$ (1) $23 \times 10^{5} ms^{- 1}$ (2) $8 \times 10^{5} m s^{- 1}$ (3) $16 \times 10^{5} m s^{- 1}$ (4) $42 \times 10^{5} m s^{- 1}$ 166. $The electrostatic potential in a charged spherical region of radius r varies as V = a r^{3} + b, where a and b are constants. The total charge in the sphere of unit radius is α \times πa \in_{o} . The value of α is____. (permittivity of vacuum is ϵ_{0})$ (1) $-9$ (2) $-12$ (3) $-8$ (4) $-6$ 167. $Force between two point charges q_{1} and q_{2} placed in vacuum at 'r' cm apart is F. Force between them when placed in a medium having dielectric K = 5 at ' r /5' cm apart will be:$ (1) $F /25$ (2) $5 F$ (3) $F/5$ (4) $25 F$ 168. $A charged particle of mass ' m ' and charge ' q ' is released from rest in an uniform electric field E . Neglecting the effect of gravity, the kinetic energy of the charged particle after ' t ' second is$ (1) $\frac{Eqm}{t}$ (2) $\frac{2 E ^{2} t ^{2}}{mq}$ (3) $\frac{E ^{2} q ^{2} t ^{2}}{2 m}$ (4) $\frac{E q ^{2} m}{2 t ^{2}}$ 169. $A solid metallic sphere has a charge +3Q. Concentric with this sphere is a conducting spherical shell having charge -Q. The radius of the sphere is ' A ' and that of the spherical shell is ' B ' (B > A) . The electric field at a distance ' R ' (A < R < B) from the centre is (ϵ_{0} = permittivity of vacuum)$ (1) $\frac{Q}{2 π ϵ _{0} R}$ (2) $\frac{3 Q}{2 π ϵ _{0} R}$ (3) $\frac{3 Q}{4 π ϵ _{0} R ^{2}}$ (4) $\frac{4 Q}{2 π ϵ _{0} R ^{2}}$ 170. $An electric dipole of moment is at the origin (0, 0, 0) . The electric field due to this dipole at r \to= (+ i^+ 3 j^+ 5 k^) note that r \to \cdot p \to= 0 is parallel to$ (1) $i^+ 3 j^- 2 k^$ (2) $3 i^+ j^+ 2 k^$ (3) $- 3 i^- j^- 2 k^$ (4) $- i^+ 3 j^+ 2 k^$ 171. $The angle between the dipole moment and electric field at any point on the equatorial plane is$ (1) $90^{\circ}$ (2) $45^{\circ}$ (3) $0^{\circ}$ (4) $180^{\circ}$ 172. $The electric field intensity at a point on the axis of an electric dipole in air is 4 NC^{- 1} . Then the electric field intensity at a point on the equatorial line which is at a distance equal to twice the distance on the axial line and if the dipole is in a medium of dielectric constant 4 is$ (1) $1 NC^{- 1}$ (2) $\frac{1}{8} NC^{- 1}$ (3) $16 NC^{- 1}$ (4) $\frac{1}{16} NC^{- 1}$ 173. $Polar molecules are the molecules [NEET 2021]$ (1) $having zero dipole moment$ (2) $acquire a dipole moment only in the presence of electric field due to displacement of charges.$ (3) $acquire a dipole moment only when magnetic field is absent$ (4) $having a permanent electric dipole moment$ 174. $Consider two charged metallic spheres S1 and S2 of radii R_{1} and R_{2}, respectively. The electric fields E_{1} (on S1) and E_{2} (on S2) on their surfaces are such that E_{1} / E_{2} = R_{1} / R_{2} . Then the ratio V_{1} (on S1) / V_{2} (on S2) of the electrostatic potentials on each sphere is$ (1) $\frac{r _{1}}{r _{2}}$ (2) $(\frac{r _{1}}{r _{2}})^{2}$ (3) $\frac{r _{2}}{r _{1}}$ (4) $(\frac{r _{2}}{r _{1}})^{2}$ 175. $Electric potential at a point P due to a point charge of 5 x 10-9 C is 50 V. The distance of P from the point charge is: (Assume, \frac{1}{4 π ϵ _{0}} = 9 x 109 N m^{2} C^{- 2})$ (1) $9 cm$ (2) $3 cm$ (3) $0. 9 cm$ (4) $90 cm$ 176. $Two metal plates are separated by 2 cm . The potentials of the plates are - 10 V and + 30 V . The electric field between the two plates is$ (1) $2000 V m^{- 1}$ (2) $500 V m^{- 1}$ (3) $3000 V m^{- 1}$ (4) $1000 V m^{- 1}$ 177. $Consider two identical metallic spheres of radius R each having charge Q and mass m . Their centers have an initial separation of 4 R . Both the spheres are given an initial speed of u towards each other. The minimum value of u, so that they can just touch each other is : (Take k = \frac{1}{4 π ϵ _{0}} and assume k Q^{2} > G m^{2} where G is the Gravitational constant)$ (1) $\frac{k Q ^{2}}{2 mR} (1 - \frac{G m ^{2}}{k Q ^{2}})$ (2) $\frac{k Q ^{2}}{4 mR} (1 - \frac{G m ^{2}}{k Q ^{2}})$ (3) $\frac{k Q ^{2}}{2 mR} (1 - \frac{G m ^{2}}{2 k Q ^{2}})$ (4) $\frac{k Q ^{2}}{4 mR} (1 + \frac{G m ^{2}}{k Q ^{2}})$ 178. $Two parallel metal plates having charges +Q and -Q face each other at a certain distance between them. If the plates are now dipped in kerosene oil tank, the electric field between the plates will$ (1) $become zero$ (2) $increase$ (3) $decrease$ (4) $remain same$ 179. $An electric dipole of mass m, charge q, and length l is placed in a uniform electric field E E_{0} i . When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be:$ (1) $\frac{1}{2 π} \frac{ml}{2 q E _{0}}$ (2) $2 π \frac{ml}{qE}$ (3) $\frac{1}{2 π} \frac{2 ml}{qE}$ (4) $2 π \frac{ml}{2 q E _{0}}$ 180. $The electric field and electric potential at a point due to a point charge are 500 NC^{- 1} and 30 V respectively, then the magnitude of the charge is$ (1) $1.3 \times 10^{- 9} C$ (2) $3 \times 10^{- 12} C$ (3) $2 \times 10^{- 10} C$ (4) $1.6 \times 10^{- 20} C$