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As shown in the figure, a metallic rod of linear density 0.45 kg m⁻¹ is lying horizontally on a smooth inclined plane which makes an angle of 45° with the horizontal. The minimum current flowing in the rod required to keep it stationary, when 0.15 T magnetic field is acting on it in the vertical upward direction, will be [Use g=10 m/s²]

Asked in JEE Main 28th July 1st Shift 2022 · Force on a wire in a field

Figure: Force on a wire in a field
Answer: (1) 30 A

Step-by-step solution

Vertical B and horizontal rod: magnetic force ILB is horizontal

Along the smooth incline: ILB cos 45°=mg sin 45°

I=(λ g tan 45°)/B=(0.45×10×1)/(0.15)=30 A

Why the other options are wrong

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