A thin ring of radius \(R\) metre has a charge \(q\) C uniformly spread on it. The ring rotates about its axis with a constant frequency of \(f\) revolutions/s. The value of magnetic induction in ${}^{}$\(\mathrm{Wb ~m^{-2}}\) at the centre of the ring is:
1. \(\frac{\mu_0 qf}{2\pi R}\)
2. \(\frac{\mu_0 q}{2\pi f R}\)
3. \(\frac{\mu_0 q}{2f R}\)
4. \(\frac{\mu_0 qf}{2R}\)

A galvanometer has a coil resistance of 100 Ω and gives a full-scale deflection for 30 mA of current. If it is to work as a voltmeter in the 30 V range, how much resistance does it require to be added?

1. 900 $\Omega$

2. 1800 $\Omega$

3. 500 $\Omega$

4. 1000 $\Omega$

A square current-carrying loop is suspended in a uniform magnetic field acting in the plane of the loop. If the force on one arm of the loop is \( \overrightarrow{F}\), what will be the net force on the remaining three arms of the loop? 

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:

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$\Omega$