A coil of one loop is made from a wire of length L and thereafter a coil of two loops is made from same wire. The ratio of magnetic field at the centre of the coils will be:
1.  1 : 4
2.  1 : 1
3.  1 : 8
4.  4 : 1

For the adjoining figure, the magnetic field at a point 'P' will be:

1. $\frac{{\mu }_0}{4\pi }\odot$

2. $\frac{{\mu }_0}{\pi }\otimes$

3. $\frac{{\mu }_0}{2\pi }\otimes$

4. $\frac{{\mu }_0}{2\pi }\odot$

A charge having q/m equal to 10⁸ c/kg and with velocity 3 × 10⁵ m/s enters into a uniform magnetic field B = 0.3 tesla at an angle 30º with the direction of field. Then the radius of curvature will be:

1. 0.01 cm

2. 0.5 cm

3. 1 cm

4. 2 cm

An electron moves in a circular orbit with a uniform speed \(v\). It produces a magnetic field \(B\) at the centre of the circle. The radius of the circle is proportional to:
1. \(\sqrt{\frac{v}{B}}\)
2. \(\frac{v}{B}\)
3. \(\frac{B}{v}\)
4. \(\sqrt{\frac{B}{v}}\)

A very long straight wire carries a current I. At the instant when a charge +Q at point P has velocity $\overrightarrow{\mathrm{v}}$, as shown, the force on the charge is

1. Along ox

2. Opposite to oy

3. Along oy

4. Opposite to ox

Resistance of a Galvanometer coil is \(8~\Omega\) and \(2~\Omega\) shunt resistance is connected with it. If main current is \(1\) A then the current flow through \(2~\Omega\) resistance will be:
1. \(0.2\) A
2. \(0.8\) A
3. \(0.1\) A
4. \(0.4\) A

A coil in the shape of an equilateral triangle of side l is suspended between the pole pieces of a permanent magnet such that $\overrightarrow{\mathrm{B}}$ is in the plane of the coil. If due to a current i in the triangle, a torque τ acts on it, the side l of the triangle will be:

1. $\frac{2}{\sqrt{3}}\left(\frac{\tau }{\mathrm{Bi}}\right)$ $$

2. $\frac{1}{\sqrt{3}}\frac{\tau }{\mathrm{Bi}}$

3. $2{\left(\frac{\tau }{\sqrt{3}\mathrm{Bi}}\right)}^{\frac{1}{2}}$

4. $\frac{2}{\sqrt{3}}{\left(\frac{\tau }{\mathrm{Bi}}\right)}^{\frac{1}{2}}$

Two long parallel wires are at a distance of \(1\) m. If both of them carry one ampere of current in the same direction, then the force of attraction on the unit length of the wires will be:
1. \(2\times10^{-7}\) N/m
2. \(4\times10^{-7}\) N/m
3. \(8\times10^{-7}\) N/m
4. \(10^{-7}\) N/m

What properties will a galvanometer that is acting as a voltmeter have?

A current-carrying coil (I = 5A, R = 10 cm) has 50 turns. The magnetic field at its centre will be:
1.  1.57 mT
2.  3.14 mT
3.  1 mT
4.  2 mT