A non -conducting ring of radius 0.5m carries a total charge of 1.11 x 10^-10 C distributed non-uniformly on its circumference producing on its circumference on the electric field. E everywhere is space.

The value of the line integral ${\int }_{l = \infty }^{l = 0} (-E.dl)$ (l = 0 being centre of ring) in volts is

• +2

• -1

• -2

• zero

32.

The turns of a solenoid, designed to provide a given magnetic flux density along its axis, are wound to fill the space between two concentric cylinders of fixed radii. How should the diameter d of the wire used be chosen so as to minimize the heat dissipated in the windings?

• Wire should be multiple of 5d

• Wire should be multiple of d/3

• the wire is independent of d

• Can't say

A long straight wire is carrying current I in the +z direction. The x-y plane contains a closed circular loop carrying current I₂ and not encircling the straight wire. The force on the loop will be

• $\frac{{\mathrm{\mu }}_0{\mathrm{I}}_1{\mathrm{I}}_0}{2\mathrm{\pi }}$

• $\frac{{\mathrm{\mu }}_0{\mathrm{I}}_1{\mathrm{I}}_0}{4\mathrm{\pi }}$

• zero

• Depends on the distance of the centre of the loop from the wire.

A certain charge Q is divided into two parts q and Q-q. How the charge Q and q must be related so that when q and (Q-q) is placed at a certain distance apart experience maximum electrostatic repulsion?

• Q = 2q

• q = 3q

• Q = 4q

• Q= 4q + c

A charged particle 'q' is shot with speed v towards another fixed charged particle Q. It approaches Q upto the closest distance r and then returns. If q were given a speed 2v, the closest distance of approach would be

• r

• 2r

• r/2

• r/4

In the given figure, what is the magnetic field induction at point O.

• $\frac{{\mathrm{\mu }}_{\mathrm{o}}\mathrm{I}}{4\mathrm{\pi r}}$

• $\frac{{\mathrm{\mu }}_{\mathrm{o}}\mathrm{I}}{4\mathrm{r}} + \frac{{\mathrm{\mu }}_{\mathrm{o}} \mathrm{I}}{2\mathrm{\pi r}}$

• $\frac{{\mathrm{\mu }}_0 \mathrm{I}}{4\mathrm{r}} + \frac{{\mathrm{\mu }}_0 \mathrm{I}}{4\mathrm{\pi r}}$

• $\frac{{\mathrm{\mu }}_0 \mathrm{I} }{4\mathrm{r}} - \frac{{\mathrm{\mu }}_0 \mathrm{I}}{4\mathrm{\pi } \mathrm{r}}$

Two identical conducting balls A and B have positive charges q₁ and q₂ respectively. But q₁ ≠ q₂. The balls are brought together so that they touch each other and then kept in their original positions. The force between them is

• less than that before the balls touched

• greater than that before the balls touched

• same as that before the balls touched

• zero

A positively charged ball hangs from a silk thread. we put a positive test charge q_o at a point and measure F/q_o, then it can be predicted that the electric field strength E

• >F/q_o

• =F/q

• <F/q_o

• Cannot be estimated

Capacitor C₁ of capacitance 1μF and capacitor C₂ of capacitance 2 μF are separately charged fully by a common battery. The two capacitors are then separately allowed to discharged through equal resistors at time t =0

• the current in each of the two discharging circuits is zero at t = 0

• the currents in the two discharging circuits at  t= 0 are equal but non-zero

• the currents in the two discharging circuits at t=0

• Capacitor C₁ loses 40% of its initial charge sooner than _C2 loses 40% of the initial charge.

A uniform electric field and a uniform magnetic field acting along the same direction in a certain region. If an electron is projected along the direction of the fields with a certain velocity, then

• It will turn towards the left of the direction of motion.

• It will turn towards the right of the direction of motion

• Its velocity will increase

• Its velocity will decrease