A long wire carrying a steady current is bent into a circular loop of one turn. The magnetic field at the center of loop is B. It is then bent into a circular coil of n turns. The magnetic field at the centre of this coil of n turns will be

1.  nB               
2.  $n^{2}B$
3.  2nB             
4. $2n^{2}B$

An electron is moving in a circular path under the influence of a transverse magnetic field of $3.57\times {10}^{-2}$ T. If the value of e/m is $1.76\times {10}^{11}$ C/kg, the frequency of revolution of the electron is

(1) 1 GHz             

(2) 100 MHz

(3) 62.8 MHz         

(4) 6.28 MHz

A square loop ABCD carrying a current i, is placed near and coplanar with a long straight conductor XY carrying a current I, the net force on the loop will be:

1. $\frac{{\mu }_{0}Ii}{2\mathrm{\pi }}$              2. $\frac{2{\mu }_{0}IiL}{3\mathrm{\pi }}$

3. $\frac{{\mu }_{0}IiL}{2\mathrm{\pi }}$            4. $\frac{2{\mu }_{0}Ii}{3\mathrm{\pi }}$

A wire carrying current l has the shape as shown in the adjoining figure. Linear parts of the wire are very long and parallel to X-axis while the semicircular portion of radius R is lying in the Y-Z plane. Magnetic field at point O is :


1. $\mathrm{B}=\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\times \frac{\mathrm{i}}{\mathrm{R}}\left(\mathrm{\pi }\hat{\mathrm{i}}+2\hat{\mathrm{k}}\right)$

2. $\mathrm{B}=-\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\times \frac{\mathrm{i}}{\mathrm{R}}\left(\mathrm{\pi }\hat{\mathrm{i}}-2\hat{\mathrm{k}}\right)$

3. $\mathrm{B}=-\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\times \frac{\mathrm{i}}{\mathrm{R}}\left(\mathrm{\pi }\hat{\mathrm{i}}+2\hat{\mathrm{k}}\right)$

4. $\mathrm{B}=\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\times \frac{\mathrm{i}}{\mathrm{R}}\left(\mathrm{\pi }\hat{\mathrm{i}}-2\hat{\mathrm{k}}\right)$

An electron moving in a circular orbit of radius r makes n rotations per second. The magnetic field produced at the centre has magnitude:

$1. \frac{{\mu }_{0}ne}{2\pi r}$
$2. Zero$
$3. \frac{n^{2}e}{r}$
$4. \frac{{\mu }_{0}ne}{2r}$

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

(1) 0.5A

(2) 0.25A

(3) 2A

(4) 1A

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) $\frac{500}{499}G$

Two similar coils of radius R are lying concentrically with their planes at right angles to each other. The currents flowing in them are I and 2I, respectively. The resultant magnetic field induction at the centre will be 

(1)$\frac{\sqrt{5}{\mu }_{0}I}{2R}$                                         

(2)$\frac{3{\mu }_{0}I}{2R}$

(3)$\frac{{\mu }_{0}I}{2R}$                                             

(4)$\frac{{\mu }_{0}I}{R}$

A millivoltmeter of 25 mV range is to be converted into an ammeter of 25 A range. The value (in ohm) of necessary shunt will be:

(1)0.001                                     

(2)0.01

(3)1                                           

(4)0.05

An alternating electric field of frequency v, 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=$\frac{mv}{e} and K=2m{\mathrm{\pi }}^2{\mathrm{v}}^2{\mathrm{R}}^2$

(2)B=$\frac{2\mathrm{\pi }mv}{e} and K=m^2{\mathrm{\pi vR}}^2$

(3)B=$\frac{2\mathrm{\pi }mv}{e} and K=2m{\mathrm{\pi }}^2{\mathrm{v}}^2{\mathrm{R}}^2$

(4)B=$\frac{mv}{e} and K=m^2{\mathrm{\pi vR}}^2$