A magnetic field of `(4.0xx10^-3hatk)T` exerts a force `(4.0hati+3.0hatj)xx10^-10N` on a particle having a charge `10^-9C` and moving in te `x-y` plane. Find the velocity of the particle.

Options

A. `-75 hati+100 hatj`
B. `-100 hati +75 hatj`
C. `25 hati+2hatj`
D. `2hati+25 hatj`

Answer

a

Explanation

From Lorentz force,
F=q(VxB)
Given, `F=(4hati+3hatj) xx10^(-10)N, q=10^(-9)C`
`B=4xx10^(-3) hatk T`
`:. (4hati+3hatj) xx10^(-10) =10^(-9) (ahati+bhatj) xx(4xx10^(-3)) hatk`
Solving, we get
`a=-75, b=100 implies v =-75 hat i+100 hatj`