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Question

A particle of mass m and change q moving with velocity V enters a region of uniform magnetic field of induction B . Then

A
Its path in the region of the field is always circular
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B
Its path in the region of the field is circular if v,B=0
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C
Its path in the region of the field is a straight line if v×B=0
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D
Distance travelled by the particle in time T does not depend on the angle between v and B
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Solution

The correct option is A Its path in the region of the field is always circular

Mass =m

Velocity =v

Charge =q

Now,

Kinetic energy of charged particle will never change whatever b the direction of projection.

F=q(v×B)

Which means angle between F and v hence between F and d is always 900

Now, work is dot product of F and d is always zero

So, no work done on charged particle by magnetic force so its kinetic energy never change

So,

The magnetic field is perpendicular to velocity, so the particle will perform a uniform circular motion and thus speed will not change and thus no change in kinetic energy.

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