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Question

# Two parallel, long wires carry currents i1 and i2 with i1>i2. When the currents are in the same direction, the magnetic field at a point midway between the wires is 10 μT. If the direction of i2 is reversed, then the field becomes 30 μT. The ratio i1i2 is:

A
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B
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C
2
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D
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Solution

## The correct option is C 2Let the point P be at a distance r from each of the wires.Magnetic field at P: B=μ02πr(i1−i2)=10 when i1∥i2Magnetic field at P: B=μ02πr(i1+i2)=30 when i1 is anti-parallel to i2From the above 2 equationsi1+i2i1−i2=3010⇒2i12i2=30+1030−10=2⇒i1i2=2

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