Two wires A & B are carrying currents I1 & I2 as shown in the figure. The separation between them is d. A third wire C carrying a current I is to be kept parallel to them at a distance x from A such that the net force acting on it is zero. The possible values of x are :

Engineering

Physics

Magnetic Field

Question

Two wires A & B are carrying currents I₁ & I₂ as shown in the figure. The separation between them is d. A third wire C carrying a current I is to be kept parallel to them at a distance x from A such that the net force acting on it is zero. The possible values of x are :

$x = (\frac{I_{1}}{I_{1} + I_{2}}) d and x = (\frac{I_{2}}{I_{1} - I_{2}}) d$

$x = (\frac{I_{1}}{I_{1} - I_{2}}) d and x = (\frac{I_{2}}{I_{1} + I_{2}}) d$

$x = (\frac{I_{2}}{I_{1} + I_{2}}) d and x = (\frac{I_{2}}{I_{1} - I_{2}}) d$

$x = \pm \frac{I_{1} d}{I_{1} - I_{2}}$

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Net force on wire carrying current I per unit length is

$\frac{μ_{0} I_{1} I}{2 πx} + \frac{μ_{0} I_{2} I}{2 π (d - x)} = 0$

$\frac{I_{1}}{x} = \frac{I_{2}}{x - d}$

$\Rightarrow x = \frac{I_{1} d}{I_{1} - I_{2}}$