Q. A $2\ \mu C$ charge moving around a circle with a frequency of ${6.25 \times 10}^{12}Hz$ produces a magnetic field 6.28 tesla at the centre of the circle. The radius of the circle is
A) 2.25 $m$
B) 0.25 $m$
C) 13.0 $m$
D) 1.25 $m$
Explanation
(d) The charge moving on a circular orbit acts like the current loop. Magnetic field at the centre of the current loop is $B = \frac{\mu_{0}2\pi\ I}{4\ \pi\ R}$
$B = \frac{\mu_{0}2\pi\ q\ v}{4\ \pi\ R}\mathbf{\ or}\ R = \frac{\mu_{0}2\pi\ q\ v}{4\ \pi\ B}$
Substituting the given values, we get
$R = \frac{4\pi \times 10^{- 7} \times 2\pi \times 2 \times 10^{- 6} \times 6.25 \times 10^{12}}{4\pi \times 6.28} = 1.25m$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.