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

Solution

The correct option is B $$\vec{v}$$ & $$\vec{B}$$ are mutually perpendicularWe 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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