An infinitely long straight conductor is bent into the shape as shown in the figure. It carries a current of \(i\) amperes and the radius of the circular loop is \(r\) metres. What will be the magnetic induction at its centre?
                 
1. \(\frac{\mu_{0}}{4 \pi} \frac{2 i}{r} \left( \pi + 1 \right)\)
2. \(\frac{\mu_{0}}{4 \pi} \frac{2 i}{r} \left(\pi - 1 \right)\)
3. zero
4. Infinite

In the figure shown below there are two semicircles of radius \(r_1\) and \(r_2\) in which a current \(i\) is flowing. The magnetic induction at the centre of \(O\) will be:

       
1. \(\frac{\mu_{0} i}{r} \left(r_{1} + r_{2}\right)\)
2. \(\frac{\mu_{0} i}{4} \left[\frac{r_{1} + r_{2}}{r_{1} r_{2}}\right]\)
3. \(\frac{\mu_{0} i}{4} \left(r_{1} - r_{2}\right)\)
4. \(\frac{\mu_{0} i}{4} \left[\frac{r_{2} - r_{1}}{r_{1} r_{2}}\right]\)

In a current-carrying long solenoid, the field produced does not depend upon:

Which one of the following gives the value of the magnetic field according to Biot-Savart’s law?

What is the magnetic field at point \(O\) in the figure?
                    
1. \(\frac{\mu_{0} I}{4 \pi r}\)
2. \(\frac{\mu_{0} I}{4 \pi r} + \frac{\mu_{0} I}{2 \pi r}\)
3. \(\frac{\mu_{0} I}{4 r} + \frac{\mu_{0} I}{4 \pi r}\)
4. \(\frac{\mu_{0} I}{4 r} - \frac{\mu_{0} I}{4 \pi r}\)

If the current is flowing in the south direction along a power line, then what will be the direction of the magnetic field above the power line (neglecting the earth's field)?

A proton and an \(\alpha\text-\)particle enter a uniform magnetic field perpendicularly at the same speed. If a proton takes \(25~\mu\text{s}\) to make \(5\) revolutions, then the periodic time for the \(\alpha\text-\)particle will be:
1. \(50~\mu\text{s}\)
2. \(25~\mu\text{s}\)
3. \(10~\mu\text{s}\)
4. \(5~\mu\text{s}\)