Question

A charged particle moving in a magnetic field `vec(B) = hat(i) - hat(j)` tesla, has an acceleration of `2 hat(i) + alpha hat(j)` at some instant. Find the value of `alpha`

Answer 1

`vec(F) = q (vec(v) xx vec(B))`
`vec(a) = (q)/(m) (vec(v) xx vec(B))`
`rArr vec(a) bot vec(B)`
Thus `vec(a).vec(B) = 0`
`rArr (2 hat(i) + alpha hat(j)).(hat(i) - hat(j)) = 0`
`rArr 2 - alpha = 0`
`rArr alpha = 2`