Electric Charges and Fields

Two infinitely long parallel plates of equal areas 6 cm² are separated by a distance of 1 cm. While one of the plates has a charge of + 10 nC and the other has − 10 nC. The magnitude of the electric field between the plates, if ${\mathrm{\epsilon }}_0 = \frac{{10}^{-9}}{36\mathrm{\pi }}$ F/m is

• 0.6 π kV/m

• 6 π kV/m

• 600 π kV/m

• 60 π V/m

The electric field strength in NC^-1 that is required to just prevent a water drop carrying a charge 1.6 x10^-19 C from falling under gravity is (g = 9.8 ms^-2, mass of water drop = 0.0016 g)

• 9.8 × 10^-16

• 9.8 × 10¹⁶

• 9.8 × 10^-13

• 9.8 × 10¹³

A cylinder of radius r and length l is placed in a uniform electric field of intensity E acting parallel to the axis of the cylinder. The total flux over curved surface area is

• $2\mathrm{\pi rE}$

• $\left(\frac{2\mathrm{\pi }}{\mathrm{l}}\right)\mathrm{E}$

• Zero

• $\frac{\mathrm{E}}{2\mathrm{\pi rl}}$

Electric lines of force about a positive point charge are

• radially outwards

• circular clockwise

• radially inwards

• parallel straight lines

An electric dipole of moment µ of 400 µC m is placed in a transverse electric field (E) of 50 Vm^-1 at an angle of 30° to E. Then, a torque of

• 10^-2 Nm acts along the direction E

• 10^-3 Nm acts along the direction µ

• 10^-2 Nm acts normal to both E and µ

• 10^-3 Nm acts along the direction E

The velocity acquired by a charged particle of mass m and charge Q accelerated from rest by a potential of V is

• $\frac{\mathrm{QV}}{\mathrm{m}}$

• $\sqrt{\frac{\mathrm{m}}{\mathrm{Qv}}}$

• $\sqrt{\frac{2\mathrm{QV}}{\mathrm{m}}}$

• mQV

An electron moving with a constant velocity v along X-axis enters a uniform electric field applied along Y-axis. Then, the electron moves

• with uniform acceleration along Y-axis

• without any acceleration along Y-axis

• in a trajectory represented as y = ax²

• in a trajectory represented as y = ax

A plane square sheet of charge of side 0.5 m has uniform surface charge density. An electron at 1 cm from the centre of the sheet experiences a force of 1.6 x 10^-12 N directed away from the sheet. The total charge on the plane square sheet is (ε₀ = 8.854 × 10^-12 C² m^-2 N^-1)

• 16.25 µC

• − 22.15 µC

• − 44.27 µC

• 144.27 µC

The time period of revolution of a charge q₁ and of mass m moving in a circular path of radius r due to Coulomb force of attraction with another charge q₂ at its centre is

• $\sqrt{\frac{16{\mathrm{\pi \epsilon }}_0{\mathrm{mr}}^3}{{\mathrm{q}}_1{\mathrm{q}}_2}}$

• $\sqrt{\frac{8{\mathrm{\pi }}^2{\mathrm{\epsilon }}_0{\mathrm{mr}}^3}{{\mathrm{q}}_1{\mathrm{q}}_2}}$

• $\sqrt{\frac{{\mathrm{\epsilon }}_0{\mathrm{mr}}^3}{16 {\mathrm{q}}_1{\mathrm{q}}_2}}$

• $\sqrt{\frac{16{\mathrm{\pi }}^3{\mathrm{\epsilon }}_0{\mathrm{mr}}^3}{{\mathrm{q}}_1{\mathrm{q}}_2}}$

When a comb rubbed with dry hair attracts pieces of paper. This is because the

• comb polarizes the piece of paper

• comb induces a net dipole moment opposite to the direction of field

• electric field due to the comb is uniform

• comb induces a net dipole moment perpendicular to the direction of field