First slide

Magnetic field due to a moving charge

Question

An electron is revolving round a proton, producing a magnetic field of 16 Wb/m² in a circular orbit of radius $1 \overset{o}{A}$ . Its angular velocity will be

Moderate

A

$10^{17} rad / s$
B

$1 / 2 π \times 10^{12} rad / s$
C

$2 π \times 10^{12} rad / s$
D

$4 π \times 10^{12} rad / s$

Solution

Magnetic field due to revolution of electron,
$\begin{array}{l} B = \frac{μ_{0}}{4 π} . \frac{2 πi}{r} = \frac{μ_{0}}{4 π} . \frac{2 π . (\frac{eω}{2 π})}{r} = 10^{- 7} \times \frac{eω}{r} \\ \Rightarrow 16 = 10^{- 7} \times \frac{1 .6 \times 10^{- 19} ω}{1 \times 10^{- 10}} \Rightarrow ω = 10^{17} rad / s \end{array}$

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