Question 225: Magnetism and Matter

Question

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 $$'	heta '$$ with the vertical. If wires have mass $$\lambda $$ per unit-length then the value of $$I$$ is : 
($$g=$$ $$gravitational$$ $$acceleration$$ )

Accepted Answer

Let us consider $$'\ell '$$ length of current carrying wire,
At equilibrium
$$T\cos 	heta  = \lambda g\ell $$
and $$T\sin 	heta  = {{{\mu _0}} \over {2\pi }}{{I 	imes Il} \over {2L\sin 	heta }}$$
$$\left[ {\,\,} ight.$$ as $$\left. {{{{F_B}} \over \ell } = {{{\mu _0}} \over {4\pi }}{{2I 	imes I} \over {2\ell \sin 	heta }}\,\,} ight]$$
Therefore, $$I = 2\sin 	heta \sqrt {{{\pi \lambda gL} \over {{u_0}\cos 	heta }}} $$

Answer

$$2\sqrt {{{\pi gL} \over {{\mu _0}}}	an 	heta } $$

Answer

$$\sqrt {{{\pi \lambda gL} \over {{\mu _0}}}	an 	heta } $$

Answer

$$\sin 	heta \sqrt {{{\pi \lambda gL} \over {{\mu _0}\,\cos 	heta }}} $$

Answer

$$2\sin 	heta \sqrt {{{\pi \lambda gL} \over {{\mu _0}\,\cos 	heta }}} $$

Magnetism and Matter

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