The magnetic field due to a current carrying circular loop of radius 3 cm at a point on the axis at a distance

Question

The magnetic field due to a current carrying circular loop of radius 3 cm at a point on the axis at a distance of 4 cm from the centre is 54 μT . What will be its value at the centre of the loop?

Accepted Answer

The magnetic field on the axis of a circular loop is

B_{a x i s} = \frac{μ _{0} I R ^{2}}{2 ( R ^{2} + x ^{2} ) ^{3/2}}

.The field at the center is

B_{ce n t er} = \frac{μ _{0} I}{2 R}

.Taking the ratio:

\frac{B _{a x i s}}{B _{ce n t er}} = \frac{R ^{3}}{( R ^{2} + x ^{2} ) ^{3/2}}

Given

R = 3 cm

,

x = 4 cm

, and

B_{a x i s} = 54 μ T

:

\frac{54}{B _{ce n t er}} = \frac{3 ^{3}}{( 3 ^{2} + 4 ^{2} ) ^{3/2}} = \frac{27}{( 25 ) ^{3/2}} = \frac{27}{125}

B_{ce n t er} = 54 \times \frac{125}{27} = 2 \times 125 = 250 μ T

The magnetic field due to a current carrying circular loop of radius $3 cm$ at a point on the axis at a distance of $4 cm$ from the centre is $54 μ T$ . What will be its value at the centre of the loop?

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The magnetic field due to a current carrying circular loop of radius 3cm at a point on the axis at a distance of 4cm from the centre is 54μT. What will be its value at the centre of the loop?