A wire carrying current I has the shape as shown in adjoining figure. Linear parts of the wire are very long and parallel to X-axis while semicircular portion of radius R is lying in Y−Z plane. Magnetic field at point O is
A
→B=−μo4πIR(π^i−2^k)
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B
→B=−μo4πIR(π^i+2^k)
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C
→B=μo4πIR(π^i−2^k)
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D
→B=μo4πIR(π^i+2^k)
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Solution
The correct option is B→B=−μo4πIR(π^i+2^k)
Magnetic field due to segment 1 →B=→B1=μ0I4πR[sin90∘+sin0∘](−^k) →B1=−μ0I4πR(^k)
Magnetic field due to segment 2 B2=μoI4πRπ(−^i)=−μoI4πR(π^i)
Magnetic field due to segment 3 →B=→B3=μ0I4πR[sin90∘+sin0∘](−^k) →B3=−μ0I4πR(^k)
Net magnetic field at O →Bc=→B1+→B2+→B3 =−μoI4πR(π^i+2^k)