Question

If we double the radius of the coil keeping the current through it unchanged, the magnetic field on its axis at very very far away points:

• A. becomes four times
• B. is doubled
• C. remains unchanged
• D. is halved

Answer 1

The correct option is A becomes four times

Magnetic field due to a circular coil of radius $a$ is given by:

$B=\frac{{\mu }_{o}I{a}^2}{2(x^2+a^2{)}^{3/2}}$

For $x>>a$,

$B\approx \frac{{\mu }_{o}I{a}^2}{2x^3}$

$⟹B\propto a^2$

As radius is doubled, magnetic field becomes four times.