Question

A wire carries a current I amperes shown in figure.The semi circle has a radius r.The magnetic field at the centre C will be

• A. Zero
• B. $\frac{\pi I}{r}\times {10}^{-7}Newton/ampere-metre$
• C. $\frac{\pi I}{r}Newton/ampere-metre$
• D. $\frac{\pi I}{r}gauss$

Answer 1

The correct option is B $\frac{\pi I}{r}\times {10}^{-7}Newton/ampere-metre$

Answer is B.
Circular wire produces magnetic field inside the circle and outside the circle. Magnetic field around a circular wire is calculated by the formula;$B=\frac{{\mu }_{0}I}{2r}where,{\mu }_0=4\pi \times {10}^{-7}N/A-m$.
since we have semicircle, we put 1/2 in front of our formula.
Therefore, the formula becomes $\frac{1}{2}\frac{4\pi \times {10}^{-7}\times I}{2r}=\frac{\pi I\times {10}^{-7}}{r}N/A-m$.
Hence, The magnetic filed at the centre C will be $\frac{\pi I}{r}\times {10}^{-7}$ Newton/ampere-metre.