Question

A straight wire carrying a current of 10 A is bent into a semi-circular arc of radius $\pi$ cm as shown in Fig. What is the magnitude and direction of the magnetic field at centre 0 of the arc?

• A. ${10}^{-4}$ T normal to the plane of the arc and directed into the page.
• B. ${10}^{-4}$ T normal to the plane of the arc and directed outside the page.
• C. $2\times {10}^{-4}$ T parallel to the plane of the arc and directed to the left.
• D. $2\times {10}^{-4}$ T parallel to the plane of the arc and directed to the right.

Answer 1

The correct option is B

${10}^{-4}$ T normal to the plane of the arc and directed outside the page.

The field at the centre 0 of the arc due to each straight portion of the wire is zero because point 0 lies on the line joining the straight portions. Thus the field at 0 is only due to half the circular loop and hence its magnitude is
$B=\frac{{\mu }_{0}I}{4r}=\frac{4\pi \times {10}^{-7}\times 10}{4\times \pi \times {10}^{-2}}={10}^{-4}T$
Since the current in the arc is in the anticlockwise sense, the field is normal to the plane of the arc and directed out of the page. Hence the correct choice is (b).