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A circular loop of radius R carries current $I_{2}$ in a clockwise direction as shown in figure. The centre of the loop is a distance $D$ above a long, straight wire. What are the magnitude and direction of the current $I_{1}$ in the wire if the magnitude field at the centre of loop is zero?
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$I_{1} = (\frac{πD}{2 R}) I_{2}, towards right$

$I_{1} = (\frac{πD}{R}) I_{2}, towards right$

$I_{1} = (\frac{πD}{3 R}) I_{2}, towards l e f t$

$I_{1} = (\frac{πD}{R}) I_{2}, towards l e f t$

answer is A.

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Detailed Solution

$I_{2}$ produces inwards magnetic field at centre. Hence, $I_{1}$ should produce outward magnetic field. Or current should be towards right. Further,

$\frac{μ_{0} I_{2}}{2 R} = (\frac{μ_{0}}{2 π}) (\frac{I_{1}}{D}) ∴ I_{1} = (\frac{πD}{R}) I_{2}$

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