Two long current carrying thin wires, both with current I, are held by insulating threads of length L and are in equilibrium as shown in the figure, with threads making an angle 'θ' with the vertical. If wires have mass λ per unit length then the value of I is : (g = gravitational acceleration)

Engineering

Physics

Magnetic Force on a Current Carrying Wire

Question

$2 \sqrt{\frac{πgL}{µ_{0}} tanθ}$

$sinθ \sqrt{\frac{πλgL}{µ_{0} cosθ}}$

$2 sinθ \sqrt{\frac{πλgL}{µ_{0} cosθ}}$

$2 \sqrt{\frac{πgL}{µ_{0}} tanθ}$

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$\frac{x}{L} = sinθ$ x = L tan $θ$

d = 2Lsin $θ$

$\frac{dF}{dℓ} = \frac{µ_{0} i_{1} i_{2}}{2 πd}$

$tanθ = \frac{µ_{0} i^{2}}{2 π 2 Lsinθλg}$

$\sqrt{\frac{4 πLsinθλgtanθ}{µ_{0}}} = i$

$i = 2 {son}^{2} θ \sqrt{\frac{πLλg}{µ_{0} cosθ}}$