Velocity and acceleration vectors of charged particle moving perpendicular to the direction of magnetic field at a given instant of time are `vecv=2hati+chatj` and `veca=3hati+4hatj` respectively. Then that value of 'c' is

Options

A. 3
B. `1.5`
C. `-1.5`
D. `-3`

Answer

C

Explanation

When a charged particle moves perpendicular to the magnetic field, it follows a circlular, path.
Here, force `q(vxxb)` is perpendicular to v and is constant in magnitude, while particle moves on a circular path. On the circular path, its velocity (v) and acceleration (a) will be at right angle to each other.
Given `v=2 hati+c hatj, a = 3hati+4 hatj`
As, v and a are perpendicular, hence,
`v*a=0(3 hati+4hatj)=0 (2hati+chatj)`.
`rArr 6+4c=0 rArr c=-1.5`