A conductor (shown in the figure) carrying constant current I is kept in the x-y plane in a uniform magnetic field . If F is the magnitude of the total magnetic force acting on the conductor, then the correct statement(s) is (are)

Engineering

Physics

Magnetic Force on a Current Carrying Wire

Question

A conductor (shown in the figure) carrying constant current I is kept in the x-y plane in a uniform magnetic field $\vec{B}$ . If F is the magnitude of the total magnetic force acting on the conductor, then the correct statement(s) is (are)

If $\vec{B}$ is along $\hat{x}$ , F = 0

If $\vec{B}$ is along $\hat{z}$ , F $\propto$ (L + R)

If $\vec{B}$ is along $\hat{y}$ , F $\propto$ (L + R)

If $\vec{B}$ is along $\hat{z}$ , F = 0

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In uniform $\vec{B}$ , random shaped conductor can also be replaced by a straight conductor of length

= L + 2R + L = 2(R + L) $\hat{i}$

(A) $\vec{F} = i \vec{ℓ} \times \vec{B} = 2i (R + L) ( (\hat{i} \times \hat{k}) B_{0} = 2iB 0 (R + L) (- \hat{j}), F \propto$ (R + L)

(B) $\vec{F} = 0 if \vec{B} = B_{0} \hat{i} as = \hat{ℓ} × \vec{B} = 0$

(D) $\vec{F} = 2 {iB}_{0} (R + L) (\hat{i} \times \hat{k}) \neq 0$