Electric Charges and Fields

Pick out the statement which is incorrect ?

• A negative test charge experiences a force opposite to the direction of the field

• The tangent drawn to a line of force represents the direction of electric field

• Field lines never intersect

• The electric field lines forms closed loop

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 spheres and kept at the same distance as before, the new force of repulsion is

• $\frac{\mathrm{F}}{3}$

• F

• $\frac{\mathrm{F}}{9}$

• 3F

A spherical shell of radius 10 cm is carrying a charge q. If the electric potential at distances 5 cm, 10 cm and 15 cm from the centre of the spherical shell is V₁, V₂ and V₃ respectively, then

• V₁ = V₂ > V₃

• V₁ > V₂ > V₃

• V₁ = V₂ < V₃

• V₁ < V₂ < V₃

If there are only one type of charge in the universe, then (E → Electric field , dS → Area vector)

• $\oint \mathrm{E} \mathrm{dS} \ne 0$ on any surface

• $\oint \mathrm{E} \mathrm{dS} \mathrm{could} \mathrm{not} \mathrm{be} \mathrm{defined}$

• $\oint \mathrm{E} \mathrm{dS} = \infty$if charge is inside

• $\oint \mathrm{E} \mathrm{dS} = 0$ if charge is outside, = $\frac{\mathrm{q}}{{\mathrm{\epsilon }}_0}$ if charge is inside

An electron of mass m, charge e falls through a distance h metre in a uniform electric field E. Then, time of fall

• $\mathrm{t} = \sqrt{\frac{2\mathrm{hm}}{\mathrm{eE}}}$

• $\mathrm{t} = \frac{2\mathrm{hm}}{\mathrm{eE}}$

• $\mathrm{t} = \sqrt{\frac{2\mathrm{eE}}{\mathrm{hm}}}$

• $\mathrm{t} = \frac{2\mathrm{eE}}{\mathrm{hm}}$

If E_ax and E_eq represents electric field at a point on the axial and equatorial line of a dipole. If points are at a distance r from the centre of the dipole, for r >> a

• E_ax = E_eq

• E_ax = − E_eq

• E_ax = − 2 E_eq

• E_eq = 2 E_ax

A particle of mass 1 g and charge 1 µC is held at rest on a frictionless horizontal surface at distance 1 m from the fixed charge 2 mC. If the particle is released, it will be repelled. The speed of the particle when it is at a distance of 10 m from the fixed charge.

• 60 ms^-1

• 100 ms^-1

• 90 ms^-1

• 180 ms^-1

The quantity of a charge that will be transferred by a current flow of 20 A over 1 h 30 min period is

• 10.8 × 10³ C

• 10.8 × 10⁴ C

• 5.4 × 10³ C

• 1.8 × 10⁴ C

Two point charges A = +3 nC and B=+ 1 nC are placed 5 cm apart in air. The work done to move charge B towards A by 1 cm is

• 2.0 × 10^-7 J

• 2.7 × 10^-7 J

• 1.21 × 10^-7 J

• 1.35 × 10^-7 J

4 x 10¹⁰ electrons are removed from a neutral metal sphere of diameter 20 cm placed in air. The magnitude of the electric field (in NC^-1) at a distance of 20 cm from its centre is

• 640

• 5760

• Zero

• 1440