The resistances of three parts of a circular loop are as shown in the figure. What will be the magnetic field at the centre of \(O\) 
(current enters at \(A\) and leaves at \(B\) and \(C\) as shown)?

 
1. \(\frac{\mu_{0} I}{6 a}\)
2. \(\frac{\mu_{0} I}{3 a}\)
3. \(\frac{2\mu_{0} I}{3 a}\)
4. \(0\)

Which of the following graphs correctly represents the variation of magnetic field induction with distance due to a thin wire carrying current?

1.		2.
3.		4.

Two similar coils of radius \(R\) are lying concentrically with their planes at right angles to each other. The currents flowing in them are \(I\) and \(2I,\) respectively. What will be the resultant magnetic field induction at the centre?
1. \(\sqrt{5} \mu_0I \over 2R\)
2. \({3} \mu_0I \over 2R\)
3. \( \mu_0I \over 2R\)
4. \( \mu_0I \over R\)

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. \(\frac{\mu_{0} I}{4 r} - \frac{\mu_{0} I}{4 \pi r}\)

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

Two identical long conducting wires \(\mathrm{AOB}\) and \(\mathrm{COD}\) are placed at a right angle to each other, with one above the other such that '\(O\)' is the common point for the two. The wires carry \(I_1\) and \(I_2\) currents, respectively. Point '\(P\)' is lying at a distance '\(d\)' from '\(O\)' along a direction perpendicular to the plane containing the wires. What will be the magnetic field at the point \(P\)?
1. \(\frac{\mu_0}{2\pi d}\left(\frac{I_1}{I_2}\right )\)
2. \(\frac{\mu_0}{2\pi d}\left[I_1+I_2\right ]\)
3. \(\frac{\mu_0}{2\pi d}\left[I^2_1+I^2_2\right ]\)
4. \(\frac{\mu_0}{2\pi d}\sqrt{\left[I^2_1+I^2_2\right ]}\)

A ring of radius \(R\) carries a linear charge density \(\lambda\). It is rotating with angular speed \(\omega\) about an axis passing through the centre and perpendicular to the plane. What is the magnetic field at its centre?
1. \(\frac{3 \mu_{0} \lambda \omega}{2}\)
2. \(\frac{\mu_{0} \lambda \omega}{2}\)
3. \(\frac{\mu_{0} \lambda \omega}{\pi}\)
4. \(\mu_{0} \lambda \omega\)