If a charged particle goes unaccelerated in a region containing electric and magnetic fields,
(i) `vec(E)` must be perpendicular to `vec(B)`
(ii) `vec(v)` must be perpendicular to `vec(E)`
(iii) `vec(v)` must be perpendicular to `vec(B)`
(iv)`E` must be equal to `v B`

Options

A. (i), (ii)
B. (ii), (iv)
C. (ii), (iii)
D. (i), (iv)

Answer

A

Explanation

The particle is moving in a straight line.
(i) `vec(E) || vec(B), vec(v)|| vec(E)`
`F_(m) = 0, F_(e) = qE`
`rarrE`
`rarr B`

The path is straight line, O.K.
(ii) `vec(E) cancel(||) vec(B)`
It may be

`F_(e) = F_(m)`, net force `= 0`
O.K.
(iii) `vec(v) || vec(B), vec(E) cancel(||) vec(B), F_(m) = 0`

The path will be parabola
(iv) `vec(E) || vec(B), vec(v) cancel(||) vec(E)`, The path will not be straight line