Magnetic Field Due to a Straight Current Carrying Conductor
Two straight ...
Question
Two straight long conductors AOB and COD are perpendicular to each other and carry currents i1 and i2. The magnitude of the magnetic induction at a point P at a distance d from the point O in a direction perpendicular to the plane ABCD is :
A
μ02πd(i1+i2)
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B
μ04πd(i1−i2)
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C
μ02πd√(i21+i22)
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D
μ02πd(i1i2i1+i2)
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Solution
The correct option is Cμ02πd√(i21+i22) Magnetic field at point P due to the wire AOB is B1=μ0I12πd Magnetic field at point P due to the wire COD is B2=μ0I22πd But, B1⊥B2 ∴B=√B21+B22=μ02πd√I21+I22