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Question

Velocity and acceleration vectors of a charged particle moving in a magnetic field at some instant are v=3^i+4^j and a=2^i+x^j (Select the correct alternative(s).

A
x=1.5
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B
x=3
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C
Magnetic field is along z - direction.
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D
Kinetic energy of the particle is constant
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Solution

The correct option is D Kinetic energy of the particle is constant
The magnetic force Fm is given by
Fm=qV×B
ma=qV×B---(i)

Using the above equation we can say a is perpendicular to both V and B.

So, a.V=0
(2^i+x^j).(3^i+4^j) = 0
6+4x=0
x=32=1.5
Both V and a are in xy plane so B must be in z direction to satisfy equation (i).
As mass and magnitude of velocity both are constant, it means kinetic energy will also be constant.

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