Question

# The force on a charged particle moving through a magnetic field is maximum when

A
Moving with the field
B
Moving against the field
C
Moving at a 45 angle to the field
D
Moving at a 90 angle to the field
E
The particle will not be affected

Solution

## The correct option is E Moving at a $$90^{\circ}$$ angle to the fieldMagnetic force on the charged particle       $$F_m =q (\vec{v} \times \vec{B}) = qvB$$ $$sin\theta$$where  $$\theta$$ is the angle between  $$\vec{v}$$  and  $$\vec{B}$$$$\therefore$$  $$F_{m}$$ is maximum when    $$sin\theta =1$$     OR     $$\theta = 90^o$$ Thus magnetic force on charged particle is maximum when it moves at a $$90^o$$ angle to the field.Physics

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