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Two identical wires R and S lie parallel in the horizontal plane, their axis being 0.10 m apart. A current of 30 A in S Neglecting the effect of the earth's magnetic flux density at a point P in the plane of the wires. If P is mid way between R and S [permeability of free space μ0=4π×107Hm1]
If total flux density is 1.6×10XT. Find X?

Solution
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(i) Midway between R and S
Field due to R, BR=μ0I2πr
Field due to S, BS=μ0I2πr
=4π×107×302π×0.05=12×105T
Direction of B due to two wires are opposite,
B=BR+BS=0
Hence, total flux density is zero.
(ii) If P is 0.05 m from R and 0.15 m from S
BR=μ0I2πr=4×1072π×0.05
=4×105T
BS=μ0I2πr=4π×107×302π×0.15
BR and BS are in the same direction
Resultant field =BS+BR=2×107(100.05+300.15)=8×104T
Hence, total flux density is 8×104Weber

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