Question

A charge q coulomb moves in a circle at n revolutions per second and the radius of the circle is r metre. Then magnetic field at the centre of the circle is

• A. $\frac{2\mathrm{\pi q}}{nr}\times {10}^{-7}Newton/(ampere-metre)$
• B. $\frac{2\mathrm{\pi q}}{r}\times {10}^{-7}Newton/(ampere-metre)$
• C. $\frac{2\pi nq}{r}\times {10}^{-7}Newton/(ampere-metre)$
• D. $\frac{2\mathrm{\pi q}}{r}\times {10}^{-7}Newton/(ampere-metre)$

Answer 1

The correct option is C

$\frac{2\pi nq}{r}\times {10}^{-7}Newton/(ampere-metre)$

The magnetic field at the centre of the circle

$=\frac{{\mu }_0}{4\pi }\times \frac{2\mathrm{\pi i}}{r}=\frac{2\pi \left(\mathrm{nq}\right)}{r}\times {10}^{-7}Newton/(ampere-metre)$