Question 110: Magnetism and Matter

Question

A wire X of length $$50 \mathrm{~cm}$$ carrying a current of $$2 \mathrm{~A}$$ is placed parallel to a long wire $$\mathrm{Y}$$ of length $$5 \mathrm{~m}$$. The wire $$\mathrm{Y}$$ carries a current of $$3 \mathrm{~A}$$. The distance between two wires is $$5 \mathrm{~cm}$$ and currents flow in the same direction. The force acting on the wire $$\mathrm{Y}$$ is

Accepted Answer

Length of wire Y is very high compared to length of wire X. So we can assume length of wire Y is infinite compare to wire X.
Magnetic field due to wire y from 5 cm from wire towards wire X is,
$$B = {{{\mu _0}{I_1}} \over {2\pi d}} = {{{\mu _0} 	imes 3} \over {2\pi  	imes 0.05}}$$
And direction of B is outward.
Now force on wire X due to wire Y,
$${F_{YX}} = {I_2}B\,l$$
$$ = 2 	imes {{{\mu _0} 	imes 3} \over {2\pi  	imes 0.05}} 	imes 5$$
$$ = 1.2 	imes {10^{ - 5}}\,N$$
Current flowing in both the wire in same direction so both wire will attract each other with equal force.
$$	herefore$$ $${F_{YX}} = {F_{XY}}$$
$$	herefore$$ $${F_{XY}} = 1.2 	imes {10^{ - 5}}\,N$$, attractive force towards wire X.

Answer

$$1.2 	imes 10^{-5} \mathrm{~N}$$ directed towards wire $$\mathrm{X}$$.

Answer

$$1.2 	imes 10^{-4} \mathrm{~N}$$ directed away from wire $$\mathrm{X}$$.

Answer

$$1.2 	imes 10^{-4} \mathrm{~N}$$ directed towards wire $$\mathrm{X}$$.

Answer

$$2.4 	imes 10^{-5} \mathrm{~N}$$ directed towards wire $$\mathrm{X}$$.

Magnetism and Matter

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