Which of the following is the correct expression of the magnetic field( $B$ ) at the centre of a circular coil of a wire, depending on the radius( $r$ ) of the coil?

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B \propto \frac{1}{r}

B \propto r

B = r

None of these

answer is A.

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Detailed Solution

B \propto \frac{1}{r}

is the correct expression.
The area around a magnet in which the force of magnetism acts around a magnetic material or a mobile charged particle is known as the magnetic field. In a circular electric current loop, the magnetic field is more concentrated in the centre than outside. The field is even more concentrated into what is known as a solenoid when multiple loops are stacked. The expression of the magnetic field at the centre of a circular coil of a wire depends on the radius of the coil is that the magnetic field is inversely proportional to the radius of the coil. And its expression is,