Question

An electron is revolving in a circular path of radius $2.0\times {10}^{-10}$ m with a uniform speed of $3\times {10}^{6}m/s$. The magnetic induction at the centre of the circular path will be

• A. $0.6T$
• B. $1.2T$
• C. $0.12T$
• D. zero

Answer 1

Answer: (B)

Current in the circular orbit: $i=\frac{qv}{2\pi r}$
Magnetic field at the center of a circular coil is
$B=\frac{{\mu }_{0}i}{2r}=\frac{4\pi \times {10}^{-7}\frac{qv}{2\pi r}}{2r}={10}^{-7}\times \frac{qv}{r^2}={10}^{-7}\frac{1.6\times {10}^{-19}\times 3\times {10}^6}{2^2\times {10}^{-20}}=1.2T$