A wire carrying current l has the shape as shown in the adjoining figure. Linear parts of the wire are very long and parallel to X-axis while the semicircular portion of radius R is lying in the Y-Z plane. Magnetic field at point O is :


1. $\mathrm{B}=\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\times \frac{\mathrm{i}}{\mathrm{R}}\left(\mathrm{\pi }\hat{\mathrm{i}}+2\hat{\mathrm{k}}\right)$

2. $\mathrm{B}=-\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\times \frac{\mathrm{i}}{\mathrm{R}}\left(\mathrm{\pi }\hat{\mathrm{i}}-2\hat{\mathrm{k}}\right)$

3. $\mathrm{B}=-\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\times \frac{\mathrm{i}}{\mathrm{R}}\left(\mathrm{\pi }\hat{\mathrm{i}}+2\hat{\mathrm{k}}\right)$

4. $\mathrm{B}=\frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }}\times \frac{\mathrm{i}}{\mathrm{R}}\left(\mathrm{\pi }\hat{\mathrm{i}}-2\hat{\mathrm{k}}\right)$

A part of a long wire carrying a current i is bent into a circle of radius r as shown in the figure. The net magnetic field at the centre O of the circular loop is

1. $\frac{{\mu }_{0}i}{4r}$                                

2. $\frac{{\mu }_{0}i}{2\mathrm{\pi r}}\left(\mathrm{\pi }+1\right)$

3. $\frac{{\mu }_{0}i}{2r}$                                

4. $\frac{{\mu }_{0}i}{2\mathrm{\pi r}}\left(\mathrm{\pi }-1\right)$

A vertical wire kept in Z-X plane carries a current from Q to P (see figure). The magnetic field due to current-carrying wire will have the direction at the origin O along :

1. OX

2. OX'

3. OY

4. OY'

A long straight wire of radius \(R\) carries a uniformly distributed current \(i.\) The variation of magnetic field \(B\) from the axis of the wire is correctly presented by the graph?

1.		2.
3.		4.

A long, straight wire carries a current along the \(z-\)axis. One can find two points in the \(X-Y\) plane such that:

Choose the correct option :