Question

# The figure shows two long parallel current carrying wires separated by a distance 5 m. The magnetic field at a point P, situated midway between the two wires will be

A
μ04π
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B
μ0π
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C
μ02π
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D
4μ0π
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Solution

## The correct option is C μ02π Magnetic field at distance r from a long current carrying wire is given by the formula, B=μ0i2πr Now, →B(due to wire 1) at point P, −→B1=μ0i12πr⨂ (into the plane) i1=5 A, r1=2.5 m −→B1=5μ02π(2.5)⨂ Assuming that the two wires lies in the x−y plane, so −→B1=μ0π(−^k) Similarly, for wire 2, magnetic field at point P, −→B2=2.5μ05π⨀ (out of the plane or ^k) −→B2=μ02π (^k) So the net magnetic field at point P is given by −→BP=−→B1+−→B2 −→BP=μ0π(−^k)+μ02π ^k −→BP=μ02π(−^k) ∴∣∣∣−→BP∣∣∣=μ02π Therefore, option (c) is the correct answer.

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