Question

A point charge $Q(=3\times {10}^{-12}C)$ rotates uniformly in a vertical circle of radius $R=1mm$. The axis of the circle is aligned along he magnetic axis of the earth. At what value of the angular speed $\omega$, the effective magnetic field at the center of the circle will be reduced to zero? (Horizontal component of Earth's magnetic field is $30$ micro Tesla).

• A. ${10}^{11}rad/s$
• B. ${10}^{9}rad/s$
• C. ${10}^{13}rad/s$
• D. ${10}^{7}rad/s$

Answer 1

The correct option is A ${10}^{11}rad/s$

Magnetic field produced by charge should be equal to earths magnetic field

$\frac{{\mu }_{o}q}{4\pi }\frac{\omega r\times r}{r^3}=30\times {10}^{-}6$

So $\omega ={10}^{11}rad/s$