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Question

A charged particle is moving with velocity $$\vec{v}$$ in a uniform magnetic field $$\vec{B}$$. The magnetic force acting on it will be maximum when __________.


A
v & B are in same direction
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B
v & B are in opposite direction
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C
v & B are mutually perpendicular
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D
v & B make an angle of 45o with each other
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Solution

The correct option is B $$\vec{v}$$ & $$\vec{B}$$ are mutually perpendicular
We know,according to Lorentz force, $$\vec{F} = q[\vec{E} + (\vec{v} \times \vec{B} )]$$.
$$\Rightarrow$$ $$\vec{F} = q v \times\vec{B}  (\because \vec{E} = 0) $$
$$\Rightarrow$$ $$\vec{F}(magnitude) = qvB\sin\theta$$
From here, we can see that  magnetic force will be maximum when $$\sin\theta$$ is maximum or $$\theta= 90^0$$.So, the magnetic force acting on it will be maximum when $$\vec{v} $$ and  $$\vec{B} $$ are mutually perpendicular.
Therefore, C is correct option.

Physics

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