Question

A long straight wire is bent into a loop as shown in figure. Find the direction and magnitude of the magnetic field at the centre $O$ of the circular portion, if the radius of the circular portion is $10cm$ and current flowing through wire is $10A$.

• A. $4.14\times {10}^{-5}T$
• B. $8.28\times {10}^{-5}T$
• C. $4.14\times {10}^{-3}T$
• D. $8.28\times {10}^{-3}T$

Answer 1

The correct option is A $4.14\times {10}^{-5}T$

Using biot-savart law, magnetic field due to a section $\overrightarrow{dl}$ is:

$\overrightarrow{dB}=\frac{{\mu }_{o}I}{4\pi r^2}dl\hat{k}$

$\overrightarrow{B}=\frac{{\mu }_{o}I}{4\pi r^2}{\int }_0^{2\pi r}dl\hat{k}$

$B=\frac{{\mu }_{o}I}{2r}$

$=\frac{2\pi \times {10}^{-7}\times 10}{.1}$

$=6.28\times {10}^{-5}T$