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:
1. | \(nB\) | 2. | \(n^2B\) |
3. | \(2nB\) | 4. | \(2n^2B\) |
1. | \(1~\text{GHz}\) | 2. | \(100~\text{MHz}\) |
3. | \(62.8~\text{MHz}\) | 4. | \(6.28~\text{MHz}\) |
A \(250\) turn rectangular coil of length \(2.1\) cm and width \(1.25\) cm carries a current of \(85~\mu\text{A}\) and subjected to the magnetic field of strength \(0.85~\text{T}\). Work done for rotating the coil by \(180^\circ\) against the torque is:
1. \(4.55~\mu\text{J} \)
2. \(2.3~\mu\text{J} \)
3. \(1.15~\mu\text{J} \)
4. \(9.4~\mu\text{J} \)
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. | \(\frac{\mu_0i^2}{2\pi d}\) | 2. | \(\frac{2\mu_0i^2}{\pi d}\) |
3. | \(\frac{\sqrt{2}\mu_0i^2}{\pi d}\) | 4. | \(\frac{\mu_0i^2}{\sqrt{2}\pi d}\) |
1. | \(7.14\) A | 2. | \(5.98\) A |
3. | \(14.76\) A | 4. | \(11.32\) A |
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 \(\text{ABCD}\) carrying a current \(i\) is placed near and coplanar with a long straight conductor \(\mathrm{XY}\) carrying a current \(I\), what will be the net force on the loop?
1. \(\frac{\mu_0Ii}{2\pi}\)
2. \(\frac{2\mu_0IiL}{3\pi}\)
3. \(\frac{\mu_0IiL}{2\pi}\)
4. \(\frac{2\mu_0Ii}{3\pi}\)
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. \(1~\text{A}\)