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Two long parallel wires are carrying currents 12 A and 8 A in the same direction. The wires are 10 cm distant apart. Where a third parallel wire must be placed so as to experience no force

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1.5 cm from P

2 cm from P

6 cm from P

3 cm from P

answer is A.

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Detailed Solution

$B_{P} = \frac{μ_{0}}{4 π} \frac{2 i}{x},$

$B_{Q} = \frac{μ_{0}}{4 π} \frac{2 i_{2}}{(0.1 - x)}$

For no net force at M,

$B_{P} = B_{Q}$

$\frac{i_{1}}{x} = \frac{i_{2}}{(0.1 - x)}$

$\frac{12}{x} = \frac{8}{0.1 - x}$

$x = 0.06 m$ from 'P'

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