Consider a circular loop (radius R ) carrying current I , the magnetic field produced by it at a point on the axis at a distance z from the centre of the loop is ( z 2 + R 2 ) 3/2 x R 2 . The value

Question

Consider a circular loop (radius R ) carrying current I , the magnetic field produced by it at a point on the axis at a distance z from the centre of the loop is ( z 2 + R 2 ) 3/2 x R 2 ​ . The value of x is

TestHub · Accepted Answer

The magnetic field at a point on the axis of a circular loop of radius $R$ carrying current $I$ , at a distance $z$ from its centre is given by Biot-Savart's law as:

$B = \frac{μ _{0} I R ^{2}}{2 ( z ^{2} + R ^{2} ) ^{3/2}}$

Comparing this with the given expression $B = \frac{x R ^{2}}{( z ^{2} + R ^{2} ) ^{3/2}}$ , we get:

$x = \frac{μ _{0} I}{2}$

Answer: $\frac{μ _{0} I}{2}$

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