An alternating electric field of frequency $\nu$, is applied across the dees (radius=R) of a cyclotron that is being used to accelerate protons (mass=m). The operating magnetic field B, used in the cyclotron and the kinetic energy (K) of the proton beam, produced by it, are given by:

1. $B=\frac{m\nu }{e}and K=2m{\mathrm{\pi }}^2{\mathrm{\nu }}^2{\mathrm{R}}^2$

2. $B=\frac{2\mathrm{\pi }m\nu }{e}and K=m^2\pi \nu R^2$

3. $B=\frac{2\mathrm{\pi }m\nu }{e}and K=2m{\mathrm{\pi }}^2{\mathrm{\nu }}^2{\mathrm{R}}^2$

4. $B=\frac{m\nu }{e}and K=m^2\pi \nu R^2$

A straight conductor carrying current I splits into two parts as shown in the figure. The radius of the circular loop is R. The total magnetic field at the centre P of the loop is,

(1)  zero

(2) $\frac{3{\mu }_{0}i}{32R}, inward$

(3) $\frac{3{\mu }_{0}i}{32R}, outward$

(4) $\frac{{\mu }_{0}i}{2R}, inward$

In an ammeter 0.2% of main current passes through the galvanometer. If resistance of galvanometer is G, the resistance of ammeter will be:

1. $\frac{1}{499}G$

2. $\frac{499}{500}G$

3. $\frac{1}{500}G$

4. $\frac{500}{499}G$

A beam of electrons passes un-deflected through mutually perpendicular electric and magnetic fields. If the electric field is switched off, and the same magnetic field is maintained, the electrons move:

1. in an elliptical orbit

2. in a circular orbit

3. along a parabolic path

4. along a straight line

When a charged particle moving with velocity $\overline{v}$ is subjected to a magnetic field of induction $\overline{B}$, the force on it is non-zero. This implies that:

1. angle between $\overline{v}$ and $\overline{B}$ is necessarily 90^o.

2. angle $\overline{v}$ and $\overline{B}$ between can have any value other than 90^o.

3. angle between $\overline{v}$ and $\overline{B}$ have any value other than zero and 180^o.

4. angle between $\overline{v}$ and $\overline{B}$ is either zero or 180^o.

A circuit contains an ammeter, a battery of 30 V, and a resistance 40.8 $\Omega$all connected in series. If the ammeter has the coil of resistance 480 $\Omega$and a shunt of 20 $\Omega$, then reading in the ammeter will be:

1. 0.5 A

2. 0.02 A

3. 2 A

4. 1 A