Question

A, B and C are parallel conductors of equal lengths carrying currents $I$, $I$ and $2I$ respectively. Distance between A and B is $x$. Distance between B and C is also $x$. $F_{1}$ is the force exerted by B on A. $F_{2}$ is the force exerted by C on A. Choose the correct answer.}

• A. $F_{1} = 2F_{2}$
• B. $F_{2} = 2F_{1}$
• C. $F_{1} = F_{2}$
• D. $F_{1} = -F_{2}$

Hint:

Force is attractive for currents in same direction, repulsive for opposite directions.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Force between two parallel conductors: $F = \frac{\mu_0 I_1 I_2}{2\pi d}$.
Step 2: Detailed Explanation:
$F_{BA} = \frac{\mu_0 I \cdot I}{2\pi x}$ (attractive, since currents in same direction). $F_{CA} = \frac{\mu_0 (2I) \cdot I}{2\pi (2x)} = \frac{\mu_0 I^2}{2\pi x}$ (repulsive, since currents in opposite direction). So $F_{BA} = F_{CA}$ but opposite in direction, hence $F_1 = -F_2$.
Step 3: Final Answer:
$F_1 = -F_2$.