Under the influence of a uniform magnetic field, a charged particle moves with constant speed \(v\) in a circle of radius \(R.\) The time period of rotation of the particle:

1.	depends on \(v\) and not on \(R.\)
2.	depends on R and not on \(v.\)
3.	is independent of both \(v\) and \(R.\)
4.	depends on both \(v\) and \(R.\)

A closed-loop \(PQRS\) carrying a current is placed in a uniform magnetic field. If the magnetic forces on segments \(PS\), \(SR\), and \(RQ\) are \(F_1, F_2~\text{and}~F_3\) respectively, and are in the plane of the paper and along the directions shown, then which of the following forces acts on the segment \(QP\)?
      

1. \(F_{3} - F_{1} - F_{2}\)

2. \(\sqrt{\left(F_{3} - F_{1}\right)^{2} + F_{2}^{2}}\)

3. \(\sqrt{\left(F_{3} - F_{1}\right)^{2} - F_{2}^{2}}\)

4. \(F_{3} - F_{1} + F_{2}\)

A particle of mass \(m\), charge \(Q\), and kinetic energy \(T\) enters a transverse uniform magnetic field of induction \(\vec B\). What will be the kinetic energy of the particle after seconds?

The resistance of an ammeter is 13 Ω and its scale is graduated for a current up to 100 A. After an additional shunt has been connected to this ammeter, it becomes possible to measure currents up to 750 A by this ammeter. The value of shunt resistance is:

1. 20 $\Omega$

2. 2 $\Omega$

3. 0.2 $\Omega$

4. 2 k$\Omega$

Under the influence of a uniform magnetic field a charged particle is moving in a circle of radius R with constant speed v. The time period of the motion:

1. depends on v and not on R.

2. depends on both R and v.

3. is independent of both R and v.

4. Depends on R and not on v.

1. \(\frac{qvR}{2}\)

2. \(qvR^{2}\)

3. \(\frac{qvR^{2}}{2}\)

4. \(qvR\)

In a mass spectrometer used for measuring the masses of ions, the ions are initially accelerated by an electric potential \(V\) and then made to describe semi-circular paths of radius \(R\) using a magnetic field \(B\). If \(V\) and \(B\) are kept constant, the ratio of \(\left(\frac{\text{Charge on the ion}}{\text{Mass of the ion}} \right)\) will be proportional to:
1. \(\frac{1}{R}\)
2. \(\frac{1}{R^2}\)
3. \(R^2\)
4. \(R\)