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Question

Magnetc field due to a current carrying circular loop of radius 12 cm at its centre is 0.5×104 T. Find the magnetic field due to this loop at a point on the axis at a distance 5.0 cm from centre.

A
3.9×105 T
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B
7.8×105 T
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C
11.7×105 T
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D
None of these
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Solution

The correct option is A 3.9×105 T
Magnetic field at the centre of the loop is given by,

B1=μ0I2R=0.5×104 T .......(1)

For an axial point,

B2=μ0IR22(R2+x2)3/2 ........(2)

From equation (1) & (2), we get

B1B2=(μ0I2R)(μ0IR22(R2+x2)3/2)

B1B2=(R2+x2)3/2R3

B2=B1[R3(R2+x2)3/2]

Putting the given data, we get

B2=0.5×104⎢ ⎢ ⎢ ⎢(12)3(122+52)32⎥ ⎥ ⎥ ⎥

B2=3.9×105 T
Why this Question ?
Key point -
The magnetic field due to a circular current carrying loop at an axial point is given by,
Baxial=μ0IR22(R2+x2)3/2

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