Question

Current is flowing in a circular coil . If the radius of the coil is doubled , then the value of magnetic field intensity at its centre will be

Answer 1

since the magnetic field in a circular coil is directly proportional to the length of the coil, if the radius of the coil is doubled the magnetic field strength also doubles

Answer 2

Explanation:

The magnetic field intensity at the center of of circular coil is given by :

$B=\dfrac{\mu_o I}{2r}$

Here,

I is current and r is radius of coil

If the radius of the coil is doubled, then new radius, r' = 2r. New magnetic field intensity is given by :

$B'=\dfrac{\mu_o I}{2r'}\\\\B'=\dfrac{\mu_o I}{2(2r)}\\\\B'=\dfrac{1}{2}\times \dfrac{\mu_o I}{2r}\\\\B'=\dfrac{1}{2}B$

So, the radius of the coil is doubled, then the magnetic field intensity at its centre will be half of the initial magnetic field.

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