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Question

Two parallel wires aligned with y- axis carrying equal currents in opposite directions are placed at x=+a and x=a in the x-y plane. The net magnetic field at the origin, O is B1 and at a point P (2a, 0, 0) is B2. Then the ratio B1:B2 is:

A
3:1
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B
1:2
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C
1:3
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D
2:1
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Solution

The correct option is A 3:1
The magnetic field at a distance 'r' from a current carrying current is given by
B=μoi2πr

Now at origin the magnetic field due to both wires will be in the same direction and as they are carrying the same current, magnetic field at origin will be :
B1=2×μ0I2πa=μ0Iπa
The magnetic field at (2a,0,0) will be :
B2=μ0I2πaμ0I6πa=μ0I3πa
B1B2=31

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