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Two Parallel Wires Separated by a Distance of 10 Cm Carry Currents of 10 a and 40 a Along the Same Direction. Where Should a Third Current by Placed So that It Experiences No Magnetic Force?

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प्रश्न

Two parallel wires separated by a distance of 10 cm carry currents of 10 A and 40 A along the same direction. Where should a third current by placed so that it experiences no magnetic force?

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उत्तर

Let the third wire W3 having current i in upward direction be placed x cm from the 10 A current wire.

The magnetic force per unit length on a wire due to a parallel current-carrying wire is given by

\[\frac{F}{l} = \frac{\mu_0 i_1 i_2}{2\pi d}\]
According to the question, wire W3 experiences no magnetic force.
∴ \[\frac{F}{l} \text{ due to wire }W_1 = \frac{F}{l} \text{ due to wire } W_2\]
\[\Rightarrow \frac{\mu_0 10i}{2\pi x} = \frac{\mu_0 40i}{2\pi(10 - x)}\]
\[ \Rightarrow 10 - x = 4x\]
\[ \Rightarrow x = 2 cm\]

Thus, wire W3 is placed 2 cm from the 10 A current wire.

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  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 35: Magnetic Field due to a Current - Exercises [पृष्ठ २५१]

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एचसी वर्मा Concepts of Physics Volume 1 and 2 [English]
अध्याय 35 Magnetic Field due to a Current
Exercises | Q 28 | पृष्ठ २५१

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