An electron is moving in a circular path under the influence of a transverse magnetic field of \(3.57\times 10^{-2}~\text{T}\). If the value of \(\frac{e}{m}\) is \(1.76\times 10^{11}~\text{C/kg}\), what will be the frequency of revolution of the electron?

1.	\(1~\text{GHz}\)	2.	\(100~\text{MHz}\)
3.	\(62.8~\text{MHz}\)	4.	\(6.28~\text{MHz}\)

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. \(1~\text{MeV}\)

A circuit contains an ammeter, a battery of \(30~\text{V},\) and a resistance \(40.8~\Omega\)$$ all connected in series. If the ammeter has a coil of resistance \(480~\Omega\)$$ and a shunt of \(20~\Omega,\)$$ then the reading in the ammeter will be:
1. \(0.5~\text{A}\)
2. \(0.02~\text{A}\)
3. \(2~\text{A}\)
4. \(1~\text{A}\)

A rectangular coil of length \(0.12~\text{m}\) and width \(0.1~\text{m}\) having \(50\) turns of wire is suspended vertically in a uniform magnetic field of strength \(0.2~\text{Wb/m}^2\). The coil carries a current of \(2~\text{A}\). If the plane of the coil is inclined at an angle of \(30^{\circ}\) with the direction of the field, the torque required to keep the coil in stable equilibrium will be:
1. \(0.15~\text{N-m}\)
2. \(0.20~\text{N-m}\)
3. \(0.24~\text{N-m}\)
4. \(0.12~\text{N-m}\)

A wire carrying current \(I\) 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 \(Y\text-Z\) plane. The magnetic field at point \(O\) is: