In the adjoining figure, two very long, parallel wires A and B carry currents of 10 ampere and 20 amperes respectively and are at a distance 20 cm apart. If a third wire C (length 15 cm) having a current of 10 ampere is placed between them, then how much force will act on C? The direction of current in all the three wires is same.

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3 × 10^–5 N (left)

6 × 10^–5 N (left)

6 × 10^–5 N (right)

3 × 10^–5 N (right)

answer is B.

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Detailed Solution

Net force on conductor R towards conductor Q will be.

$= F_{2} - F_{1} = \frac{μ_{0}}{4 π} \frac{2 I_{2} I_{3}}{r} l - \frac{μ_{0}}{4 π} \frac{2 I_{1} I_{3}}{r} l = \frac{μ_{02} I_{3} l}{4 π r} [I_{2} - I_{1}] = \frac{10^{- 7} \times 2 \times 10 \times 0 \cdot 15 (20 - 10)}{0 \cdot 10} = 3 \cdot 0 \times 10^{- 5} N towards right$