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 F₁, F_2, and F₃ 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. ${\mathrm{F}}_3-{\mathrm{F}}_1-{\mathrm{F}}_2$

2. $\sqrt{{\left({\mathrm{F}}_3-{\mathrm{F}}_1\right)}^2+{\mathrm{F}}_2^2}$

3. $\sqrt{{\left({\mathrm{F}}_3-{\mathrm{F}}_1\right)}^2-{\mathrm{F}}_2^2}$

4. ${\mathrm{F}}_3-{\mathrm{F}}_1+{\mathrm{F}}_2$

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.

If a charged particle (charge q) is moving in a circle of radius R at a uniform speed v, then the value of its associated magnetic moment μ will be:

1. $\frac{\mathrm{qvR}}{2}$

2. ${\mathrm{qvR}}^2$

3. $\frac{{\mathrm{qvR}}^2}{2}$

4. $\mathrm{qvR}$

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 \(\big(\frac{\text{Charge on the ion}}{\text{Mass of the ion}} \big)\) will be proportional to:

1. $\frac{1}{R}$

2. $\frac{1}{R^2}$

3. $R^2$

4. R