A proton carrying \(1~\text{MeV}\) kinetic energy is moving in a circular path of radius \(R\) in a uniform magnetic field. What should be the energy of an \(\alpha \text- \)particle to describe a circle of the same radius in the same field?
1. \(1~\text{MeV}\)
2. \(0.5~\text{MeV}\)
3. \(4~\text{MeV}\)
4. \(2~\text{MeV}\)

A galvanometer of resistance, \(\mathrm G,\) is shunted by the resistance of \(\mathrm S\) ohm. How much resistance is to be put in series with the galvanometer to keep the main current in the circuit unchanged?

Charge q is uniformly spread on a thin ring of radius R. The ring rotates about its axis with a uniform frequency of f Hz. The magnitude of magnetic induction at the centre of the ring is:

1. $\frac{{\mathrm{\mu }}_0\mathrm{qf}}{2\mathrm{\pi R}}$

2. $\frac{{\mathrm{\mu }}_0\mathrm{qf}}{2\mathrm{R}}$

3. $\frac{{\mathrm{\mu }}_0\mathrm{q}}{2\mathrm{fR}}$

4. $\frac{{\mathrm{\mu }}_0\mathrm{q}}{2\mathrm{\pi fR}}$

A square loop, carrying a steady current I, is placed in a horizontal plane near a long straight conductor carrying a steady current I1 at a distance d from the conductor as shown in the figure. The loop will experience:

A current loop consists of two identical semicircular parts each of radius R, one lying in the x-y plane and the other in x-z plane. If the current in the loop is I, then the resultant magnetic field due to the two semicircular parts at their common centre is:

1. $\frac{{\mu }_{0}i}{2R}$

2. $\frac{{\mu }_{0}i}{4R}$

3. $\frac{{\mu }_{0}i}{\sqrt{2}R}$

4. $\frac{{\mu }_{0}i}{2\sqrt{2}R}$

A closely wound solenoid of 2000 turns and an area of cross-section of 1.5 × 10^–4 m² carries a current of 2.0 A. It is suspended through its centre and perpendicular to its length, allowing it to turn in a horizontal plane in a uniform magnetic field of 5 × 10^–2 Tesla, making an angle of 30^o with the axis of the solenoid. What will be the torque on the solenoid?

1. 1.5 × 10^–3 Nm

2. 1.5 × 10^–2 Nm

3. 3 × 10^–2 Nm

4. 3 × 10^–3 Nm

A particle having a mass of \(10^{-2}\) kg carries a charge of \(5\times 10^{-8}~\mathrm{C}\). The particle is given an initial horizontal velocity of \(10^5~\mathrm{ms^{-1}}\) in the presence of electric field \(\vec{E}\) and magnetic field \(\vec{B}\) . To keep the particle moving in a horizontal direction, it is necessary that:
 

Which one of the following pairs of statements is possible?

Two circular coils 1 and 2 are made from the same wire but the radius of the 1^st coil is twice that of the 2^nd coil. What is the ratio of the potential difference applied across them so that the magnetic field at their centres is the same?
1. 3
2. 4
3. 6
4. 2