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Question

The magnetic induction at point O in the following figure will be -


A
μ0I4r[32+1π]
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B
μ0I4r[32+1π]
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C
μ0I4r[321π]
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D
μ0I4r[321π]
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Solution

The correct option is C μ0I4r[321π]

Net magnetic field,

B=B1+B2+B3 ...(1)

B1=0 ...(2)

B2=μ0I2rθ2π=μ0I2r×3π/22π

B2=3μ0I8r ...(3)

B3=μ0I4πr[sinθ1+sinθ2]

=μ0I4πr [sin0+sin90]

=μ0I4πr ...(4)

From (1),(2),(3) and (4),

B=0+[321π]μ0I4r

B=μ0I4r [321π]

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