Question

A charged particle of mass 1 kg is projected with initial velocity `(3hati + 4hatj)`m/s in an uniform electric field,`vecE = (-2.5hati)` N/C and gravitational field, `vecg = (-10hatj)m/s^2` ?

What should be the value of charge so that the particle moves in straight line?
a 1C
b 3C
c 5C
d 7.5C

Answer 1

Direction of initial velocity is given by `tan theta=4/3`
where `theta` is the angle made with the positive `x`-axis

Electrical force on a charge `q` is given as `vec(F_e)=qvecE=-2.5qhati`
Gravitational force on the particle is given as `vec(F_g)=mvecg=-10hatj`
Direction of resultant force `=tantheta_f=(-10)/(-2.5q)=4/q`

For the particle to move in a straight line the initial velocity and resultant force must be collinear.
For `theta=theta_f` we have

`4/3=4/q`
`=>q=3\ C`