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 charged particle goes unaccelerated
i.e net force `= 0`
`vec(F) = vec(F)_(e) + vec(F)_(m) = qvec(E) + qvec(v) xx vec(B) = 0`
`vec(E) = -(vec(v) xx vec(B))`
i.e. `vec(E)` is `_|_^(ar)` to `vec(v)` as well as `vec(B)`
`|vec(E)| = |-vec(v) xx vec(B)| rArr E = vB sin theta`