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Question

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

A

250

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B

150

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C

125

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D

72

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Solution

## The correct option is A 250 Given x = 4 cm = 0.04 m and r = 3 cm = 0.03 m. The magnetic field at a point on the axis of the loop is given by B=μ0 I r22(r2+x2)32 (1) Magnetic field at the centre of the coil is given by B0=μ0I2r (2) Dividing (1) by (2), we get B0B=r3(r2+x2)32 Substituting the values of r and x, we get B0B=12527 orB0=12527 B=12527×54 μ T=250 μ T Hence the correct choice is (a).

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