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Question

A circular loop of radius R carries current I2 in a clockwise direction, as shown in the figure. The centre of the loop is at a distance D above a long straight wire. What should be the magnitude and direction of the current I1 in the straight wire so that the net magnetic field at the centre of the loop is zero?


A
πDRI2 ()
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B
πDRI2 ()
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C
πD4RI2 ()
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D
πD4RI2 ()
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Solution

The correct option is A πDRI2 ()
The magnetic field at the centre of the loop due to the current in the loop is,

B2=μoI22R Inwards()

For the net field at the centre to be zero, the field B1, due to the straight conductor should be directed opposite to B2 i. e. normally outwards.

B1=μoI12πD Outwards()

To produce this field, the direction of current I1 must be towards right.

Thus, B1=B2

μoI12πD=μoI22R

I1=πDRI2 ()

Hence, option (a) is the correct answer.

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