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Question

A current i ampere flows in a circular arc of wire which subtends an angle (3π2) radius at its centre, whose radius is R. The magnetic induction B at the centre is :

A
μ0iR
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B
μ0i2R
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C
2μ0iR
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D
3μ0i8R
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Solution

The correct option is D 3μ0i8R
Step 1: Magnetic field due to the arc subtending an angle
At the centre :
Magnetic field due to complete circle i.e for angle 2π : B=μoi2R
Magnetic field due to unit angle: B=12π×μoi2R
Magnetic field due to θ angle: B=θ2π×μoi2R
B=θμoi4πR
[Note: Above result can directly be used for finding magnetic field at centre of an arc subtending an angle θ]

Step 2: Putting values
θ=3π2
B=3μoi8R

Hence , Option(D) is correct

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