Electrostatics PYQs Set 5 (PDF)

Set 5 of 13 · Questions 121-150 of 385

In the print window choose “Save as PDF”. The file prints without a web address or date line.

Mere Teacher · Previous Year Questions JEE Main Physics · Electrostatics · Set 5 (Q121-150)
Scan or visit mereteacher.com for free PYQ practice, timed CBT tests, step-by-step solutions and BroBot AI. Answers and solutions are free with a sign-up.
121. $An electric dipole is placed at an angle of 30^{\circ} with an electric field of intensity 2 \times 10^{5} NC^{- 1} . It experiences a torque equal to 4 N m. Calculate the magnitude of charge on the dipole, if the dipole length is 2 cm. [NEET 2023, 2016]$ (1) $6 mC$ (2) $4 mC$ (3) $2 mC$ (4) $8 mC$ 122. $Point charges + 4 q, - q and + 4 q are kept on the X ‐axis at point x = 0, x = a and x = 2 a respectively. Then$ (1) $only - q is in stable equilibrium$ (2) $all the charges are in stable equilibrium$ (3) $all of the charges are in unstable equilibrium$ (4) $none of the charges is in equilibrium$ 123. $A particle of mass m and charge q is in an electric and magnetic field given by E = 2 i + 3 j; B = 4 i + 6 j . The charged particle shifted from the origin to the point P (x = 1; y = 1) along a straight path. The magnitude of the total work done is:$ (1) $(0.35) q$ (2) $5q$ (3) $(2.5) q$ (4) $(0.15) q$ 124. $An electric dipole is formed by two equal and opposite charges q with separation d. The charges have same mass m. It is kept in a uniform electric field E. If it is slightly rotated from its equilibrium orientation, then its angular frequency ω is:-$ (1) $\frac{qE}{md}$ (2) $\frac{2 qE}{md}$ (3) $2 \frac{qE}{md}$ (4) $\frac{qE}{2 md}$ 125. $The top of the atmosphere is at about 400 kV with respect to the surface of the earth, corresponding to an electric field that decreases with altitude. Near the surface of the earth, the field is about 100 V m^{- 1} . Still, we do not get an electric shock as we step out of our house into the open house because (assume the house to be a steel cage so that there is no field inside)$ (1) $there is a potential difference between our body and the ground$ (2) $100 V m^{- 1} is not a high electric field so that we do not feel the shock$ (3) $our body and the ground forms an equipotential surface$ (4) $the atmosphere is not a conductor.$ 126. $In a region the potential is represented by V(x, y, z) = 6x - 8xy -8y + 6yz, where V is in volts and x, y, z, are in meters. The electric force experienced by a charge of 2 coulomb situated at point (1, 1,1) is:$ (1) $65 N$ (2) $30N$ (3) $24N$ (4) $435 N$ 127. $Two opposite charges each of the magnitude 500 μC are 10 cm apart. Find electric field intensity at a distance of 25 cm from the midpoint on axial line of the dipole.$ (1) $5.76 \times 10^{7} NC^{- 1}$ (2) $9.28 \times 10^{7} NC^{- 1}$ (3) $13.1 \times 10^{10} NC^{- 1}$ (4) $20.5 \times 10^{7} NC^{- 1}$ 128. $Three infinitely long wires with linear charge density λ are placed along the x - axis, y axis and z-axis respectively. Which of the following denotes an equipotential surface?$ (1) $xyz = constant$ (2) $xy + yz + zx = constant$ (3) $(x^{2} + y^{2}) (y^{2} + z^{2}) (z^{2} + x^{2}) = constant$ (4) $(x + y) (y + z) (z + x) = constant$ 129. $The potential is varying with distance (x) as V = \frac{1}{2} (y^{2} - 4 x) volt. The electric field at x = 1 m and y = 1 m is$ (1) $2 i + j Vm^{- 1}$ (2) $- 2 i + j V m^{- 1}$ (3) $2 i - j Vm^{- 1}$ (4) $- 2 i + 2 j Vm^{- 1}$ 130. $The flux of the electric field E = 24 i + 30 j + 28 k NC^{- 1} through an area of 20 m^{2} on the yz plane is$ (1) $480 Nm^{2} C^{- 1}$ (2) $600 Nm^{2} C^{- 1}$ (3) $560 Nm^{2} C^{- 1}$ (4) $1640 Nm^{2} C^{- 1}$ 131. $The potential of the electric field produced by a point charge at any point (x, y, z) is given by V = 3 x^{2} + 5, where x, y, z are in meters and V is in volts. The intensity of the electric field at (- 2, 1, 0) is$ (1) $+ 17 V m^{- 1}$ (2) $- 17 V m^{- 1}$ (3) $+ 12 V m^{- 1}$ (4) $- 12 V m^{- 1}$ 132. $The magnitude of point charge due to which the electric field 30 cm away has the magnitude 2 N C^{- 1} will be$ (1) $2 \times 10^{- 11} C$ (2) $3 \times 10^{- 11} C$ (3) $5 \times 10^{- 11} C$ (4) $9 \times 10^{- 11} C$ 133. $If V is the gravitational potential due to sphere of uniform density on its surface, then its value at the centre of sphere will be:$ (1) $\frac{4}{3} V$ (2) $\frac{V}{2}$ (3) $V$ (4) $\frac{3 V}{2}$ 134. $A system of 2 capacitors of capacitance 2 μF and 4 μF is connected in series across a potential difference of 6 V . The electric charge and energy stored in the system are$ (1) $1 μC and 3 μJ$ (2) $8 μC and 24 μJ$ (3) $10 μC and 30 μJ$ (4) $36 μC and 108 μJ$ 135. $Electric potential due to a space is given by φ (x, y, z) = φ_{0} \frac{x _{0}}{x}; when x_{0} = 5 m and φ_{0} = 8 V . Find the electric field at (10 m, 5 m, 5 m)$ (1) $0.40 Vm^{- 1} i$ (2) $- 0.40 Vm^{- 1} i$ (3) $4.0 Vm^{- 1} i$ (4) $- 4.0 Vm^{- 1} i$ 136. $Two fixed charges A and B of 5 μC each are separated by a distance of 6 m . C is the mid point of the line joining A and B. A charge ' Q ' of - 5 μC is shot perpendicular to the line joining A and B through C with a kinetic energy of 0.06 J . The charge ' Q' comes to rest at a point D. The distance CD is$ (1) $3 m$ (2) $3 m$ (3) $33 m$ (4) $4 m$ 137. $A hollow metal sphere of radius R is uniformly charged. The electric field due to the sphere at a distance r from the center$ (1) $decreases a sr increases for r<R and for r>R$ (2) $increases a sr increases for r<R and for r>R$ (3) $zero as r increases for r < R, decreases as r increases for r > R$ (4) $zero a sr increases for r < R, increases as r increases for r > R$ 138. $Two-point charges of 1 nC and 2 nC are placed at the two corners of equilateral triangle of side 3 cm. The work done in bringing a charge of 3 nC from infinity to the third corner of the triangle is μJ . \frac{1}{4 π ϵ _{0}} = 9 \times 10^{9} N . \frac{m ^{2}}{C ^{2}}$ (1) $27$ (2) $5.4$ (3) $2.7$ (4) $3.3$ 139. $A hot filament liberates an electron with zero initial velocity. The anode potential is 1200 V . The speed of the electron when it strikes the anode is$ (1) $2.1 \times 10^{7} m s^{- 1}$ (2) $2.5 \times 10^{8} m s^{- 1}$ (3) $1.5 \times 10^{5} m s^{- 1}$ (4) $2.5 \times 10^{6} m s^{- 1}$ 140. $Two conducting spheres of radii r_{1} and r_{2} are charged to the same surface charge density. The ratio of electric fields near their surfaces is$ (1) $\frac{r _{1}^{2}}{r _{2}^{2}}$ (2) $\frac{r _{2}^{2}}{r _{1}^{2}}$ (3) $\frac{r _{1}}{r _{2}}$ (4) $1 : 1$ 141. $A certain charge 2Q is divided at first into two parts q_{1} and q_{2} . Later the charges are placed at a certain distance. If the force of interaction between two charges is maximum then \frac{Q}{q _{1}} =$ (1) $1$ (2) $4$ (3) $0.5$ (4) $2$ 142. $A ball of mass 1 g having a charge of 20 μC is tied to one end of a string of length 0.9 m can rotate in a vertical plane in a uniform electric field 100 NC^{- 1} directed upwards. The minimum horizontal velocity that must be given to the ball at the lowest position so that it completes the vertical circle is (Let, g = 10 ms^{- 2})$ (1) $9 ms^{- 1}$ (2) $18 ms^{- 1}$ (3) $36 ms^{- 1}$ (4) $6 ms^{- 1}$ 143. $Two capacitors of capacity 4 μF and 6 μF are connected in series to a 500 V battery. The potential difference across 4 μF capacitor is$ (1) $200 V$ (2) $300 V$ (3) $400 V$ (4) $500 V$ 144. $A short electric dipole has a dipole moment of 16 \times 10^{- 9} C - m . The electric potential due to the dipole at a point at a distance of 0.6 m from the centre of the dipole, situated on a line making an angle of 60^{\circ} with the dipole axis is (\frac{1}{4 π ϵ _{0}} = 9 \times 10^{9} Nm^{2} / C^{2}) [NEET 2020]$ (1) $200 V$ (2) $400 V$ (3) $zero$ (4) $50 V$ 145. $The electric field due to a short electric dipole at a large distance (r) from center of dipole on the equatorial plane varies with distance as:$ (1) $r$ (2) $\frac{1}{r ^{2}}$ (3) $\frac{1}{r ^{3}}$ (4) $\frac{1}{r}$ 146. $A small block of mass 5 g and charge 5 μC is placed on insulated, frictionless, inclined plane of angle 60^{\circ} . An electric field is applied parallel to the inclined plane. If the block remains at rest then the magnitude of electric field is [ Take (g = 10 m / s^{2})$ (1) $\frac{10 ^{5}}{3} N / C$ (2) $\frac{5}{3} \times 10^{4} N / C$ (3) $3 \times 10^{4} N / C$ (4) $None$ 147. $The electric field intensity at a point near and outside the surface of a charged conductor of any shape is ' E_{1}'. The electric field intensity due to uniformly charged infinite thin plane sheet is ' E_{2}'. The relation between ' E_{1}' and ' E_{2}' is$ (1) $2 E_{1} = E_{2}$ (2) $E_{1} = E_{2}$ (3) $E_{1} = 2 E_{2}$ (4) $E_{1} = 4 E_{2}$ 148. $An electric dipole of dipole moment is 6. 0 x 1 0^{- 6} C m placed in a uniform electric field of 1.5 x 1 0^{3} N C^{- 1} in such a way that dipole moment is along electric field. The work done in rotating dipole by 180° in this field will be_______mJ.$ 149. $The electric potential at the surface of an atomic nucleus (z = 50) of radius 9 \times 10^{- 13} cm is______\times 10^{6} V$ 150. $The volume charge density of a sphere of radius 6 m is 2 µC c m^{- 3} . The number of lines of force per unit surface area coming out from the surface of the sphere is ______x 1 0^{10} N C^{- 1} .[Given : Permittivity of vacuum \in_{0} = 8.85x 1 0^{- 12} C^{2} N^{- 1} - m^{- 2}]$