Question

how will the magnetic field intensity at the centre of a circular coil carrying current change if the current carrying through the coil is doubled and the radius of the coil is halved

Answer 1

At the center of a current carrying coil, the magnetic field intensity is directly proportional to the current and inversely proportional to the radius of the coil.
So, if the current is doubled and radius is halved, then the value of B increases by 4 times the initial value.

Answer 2

Answer:

The new magnetic field will be 4B.

Explanation:

This question can be easily solved by the direct formula of the magnetic field at the center of the circular coil.

The required formula is,

B=μI/2R

B=magnetic field intensity

μ=permeability of free space=4π x $10^{-7}$

I=current through the coil

R=radius of the coil

as per the question current through the coil is doubled and radius is halved then-new expression will be

B'=μ x 2I/2 x R/2

B'=μ X 4I/2R

B'=4B