First slide

Force on a current carrying wire placed in a magnetic field

Question

A, B and C are parallel conductors of equal length carrying currents I, I and 2I, respectively. Distance between A and B is x. Distance between B and C is also x. F₁ is the force exerted by B on A and F₂ is the force exerted by C on A. Choose the correct option.

Moderate

A

F₁ = 2F₂
B

F₂ = 2F₁
C

F₁ = F₂
D

$F_{1} = - F_{2}$

Solution

$\begin{array}{l} F = \frac{μ_{0}}{4 π} = \frac{2 I_{1} I_{2}}{a} \times l \\ F_{1} = \frac{μ_{0}}{4 π} = \frac{2 I^{2}}{x} \times l (Attraction) \\ F_{2} = \frac{μ_{0}}{4 π} \times \frac{2 \times I \times 2 I}{2 x} \times l = \frac{μ_{0}}{4 π} \times \frac{2 I^{2}}{x} (Repulsion) \\ Thus F_{1} = - F_{2} \end{array}$

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