Question

An infinite straight conductor is kept along X'X axis and carries a current I. A charge q at point P(0, r) starts moving with velocity `vecv = V_0hatj` as

shown in figure. Find the direction and magnitude of force initially experienced by the charge. 

Answer 1

Magnetic field due to an infinite straight conductor in the upper region of X'X-axis,

`B = (mu_0I)/(2 pi r)hatk`

A charge q at point P(0, r) starts moving with velocity `v = v_0hatj`

Force of charge q due to straight conductor wire,

F = q (v × B)

`F = q[(v_0hatj) xx ((mu_0I)/(2 pi r) hatk)]`

⇒ `F = q[(mu_0v_0I)/(2 pi r) (hatj xx hatk)]`

`F = (qmu_0v_0I)/(2ppir)hati   ...(because hatj xx hatk = hati)`