An infinitely long straight wire and a circular loop carrying currents I1 and I2 respectively are in the same plane field at the centre of the loop is zero then

field due to straight conductor at 2R=μ0I12π×2R= field due to circular conductor at the center=μ0I22Rμ0I12π×2R=μ0I22RI1=2πI2

An infinitely long straight wire and a circular loop carrying currents I1 and I2 respectively are in the same plane field at the centre of the loop is zero then

field due to straight conductor at 2R=μ0I12π×2R= field due to circular conductor at the center=μ0I22Rμ0I12π×2R=μ0I22RI1=2πI2

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An infinitely long straight wire and a circular loop carrying currents I₁ and I₂ respectively are in the same plane field at the centre of the loop is zero then

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$I_{1} = 2 π I_{2}$

$I_{1} = I_{2}$

$I_{1} = 2 I_{2}$

$I_{2} = 2 π I_{2}$

answer is C.

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Detailed Solution

$field due to straight conductor at 2 R = \frac{μ_{0} I_{1}}{2 π \times 2 R} = field due to circular conductor at the center = \frac{μ_{0} I_{2}}{2 R}$

$\frac{μ_{0} I_{1}}{2 π \times 2 R} = \frac{μ_{0} I_{2}}{2 R}$

$I_{1} = 2 {πI}_{2}$

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