Question:
Three long straight parallel wires carrying currents are arranged as shown. The wire C carries a current \(50\) A is so placed that it experiences no force. The distance of wire C from wire A in cm is
Three long straight parallel wires carrying currents are arranged as shown. The wire C carries a current \(50\) A is so placed that it experiences no force. The distance of wire C from wire A in cm is
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Parallel currents attract, so wire C feels no force when the pulls from A and B are equal and opposite.
Updated On: Nov 12, 2026
- \(9\)
- \(7\)
- \(5\)
- \(3\)
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Concept
From the figure, A (15 A), C (50 A) and B (10 A) carry currents in the same direction, and A and B are 15 cm apart. Wire C is at a distance x from A and 15 - x from B. Parallel currents attract.
Step 2: Force Balance
Force per unit length from A on C: \(\dfrac{\mu_{0}}{2\pi}\dfrac{15\times 50}{x}\) and from B on C: \(\dfrac{\mu_{0}}{2\pi}\dfrac{10\times 50}{15-x}\).
These act in opposite directions, so they must be equal.
Step 3: Calculation
\(\dfrac{15}{x}=\dfrac{10}{15-x}\)
\(225-15x=10x\Rightarrow x=9\) cm
Step 4: Compare the options
The distance is 9 cm, option (A).
Final Answer:
Wire C is 9 cm from wire A. \[ \boxed{\text{(A) }9} \]
From the figure, A (15 A), C (50 A) and B (10 A) carry currents in the same direction, and A and B are 15 cm apart. Wire C is at a distance x from A and 15 - x from B. Parallel currents attract.
Step 2: Force Balance
Force per unit length from A on C: \(\dfrac{\mu_{0}}{2\pi}\dfrac{15\times 50}{x}\) and from B on C: \(\dfrac{\mu_{0}}{2\pi}\dfrac{10\times 50}{15-x}\).
These act in opposite directions, so they must be equal.
Step 3: Calculation
\(\dfrac{15}{x}=\dfrac{10}{15-x}\)
\(225-15x=10x\Rightarrow x=9\) cm
Step 4: Compare the options
The distance is 9 cm, option (A).
Final Answer:
Wire C is 9 cm from wire A. \[ \boxed{\text{(A) }9} \]
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