Q. The magnetic field at the centre of a current carrying circular loop is $B.$ If the radius of the loop is doubled, keeping the current same, the magnetic field at the centre of the loop would be
A) $\frac{B}{4}$
B) $\frac{B}{2}$
C) $2B$
D) $4B$
Explanation
(b) Magnetic field at the centre of current carrying loop
$B = \frac{\mu_{0}i}{2r}$ …(i)
Where $r$ is the radius of loop and $i$ the current.
Given, $r_{2} = 2r$
$\therefore\ \ \ \frac{B_{1}}{B_{2}} = \frac{1}{r} \times \frac{2r}{1} = \frac{2}{1}$
$\Rightarrow \ \ B_{2} = \frac{B_{1}}{2} = \frac{B}{2}$
Hence, magnetic field is halved.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.