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Question:

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:

→B=μ04πIR(π^i−^k)

→B=−μ04πIR(π^i+2^k)

→B=μ04πIR(π^i+2^k)

→B=−μ04πIR(π^i−^k)

Solution:

The wires are semi infinite.The magnetic field produced by each is in −^kdirection.Magnetic field produced by each wire isB=12×μ0i2πRTotal magnetic field produced by wires is→Bwires=2×12×μ0i2πR(−^k)→Bsemicircle=12μ0i2R(−^i)∴→B=→Bwires+→Bsemicircle=2×12×μ0i2πR(−^k)+12μ0i2R(−^i)=−μ04πIR(π^i+2^k)