Question

If we double the radius of a coil keeping the current through it unchanged, then the magnetic field at any point at a large distance from centre becomes approximately

• A. Double
• B. Three times
• C. Four times
• D. One - fourth

Answer 1

The correct option is C Four times

We know that magnetic field at an axial point $(d>>R)$ is given by

$B=\left(\frac{{\mu }_{0}I}{2d^3}\right)R^2$

Keeping $I$ and $d$ as constant, we get

$B\propto R^2$

Thus, when radius is doubled, the magnetic field becomes four times.

Hence, option $\left(c\right)$ is correct.