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 long wire carrying a steady current is bent into a circular loop of one turn. The magnetic field at the centre of the 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:

An arrangement of three parallel straight wires placed perpendicular to the plane of paper carrying the same current in the same direction is shown in the figure. The magnitude of force per unit length on the middle wire \(B\) is given by:
    
1. \(\dfrac{\mu_0i^2}{2\pi d}\)
2. \(\dfrac{2\mu_0i^2}{\pi d}\)
3. \(\dfrac{\sqrt{2}\mu_0i^2}{\pi d}\)
4. \(\dfrac{\mu_0i^2}{\sqrt{2}\pi d}\)

The current sensitivity of a moving coil galvanometer is \(5~\text{div/mA}\) and its voltage sensitivity (angular deflection per unit voltage applied) is \(20~\text{div/V}.\) The resistance of the galvanometer is: 
1. \(40~\Omega\)
2. \(25~\Omega\)
3. \(250~\Omega\)
4. \(500~\Omega\)

If a square loop \({ABCD}\) carrying a current \(i\) is placed near and coplanar with a long straight conductor \({XY}\) carrying a current \(I,\) what will be the net force on the loop?
                  
1. \(\dfrac{\mu_0Ii}{2\pi}\)
2. \(\dfrac{2\mu_0IiL}{3\pi}\)
3. \(\dfrac{\mu_0IiL}{2\pi}\)
4. \(\dfrac{2\mu_0Ii}{3\pi}\)

Moving perpendicular to field \(B\), a proton and an alpha particle both enter an area of uniform magnetic field \(B\). If the kinetic energy of the proton is \(1~\text{MeV}\) and the radius of the circular orbits for both particles is equal, the energy of the alpha particle will be:
1. \(4~\text{MeV}\)
2. \(0.5~\text{MeV}\)
3. \(1.5~\text{MeV}\)
4. \(1~\text{MeV}\)