A magnetic field of `(4.0xx10^-3hatk)T` exerts a force `(4.0hati+3.0hatj)xx10^-10N` on a particle having a charge `10^-9C` and moving in te `x-y` plane. Find the velocity of the particle.

Explanation

Magnetic force` vecF_m = (4.0 hati + 3.0 hatj) xx 10^(-10) N`
Let velocity of the particlein x -y plane be
`vecv = v_x hati + v_y hatj` Then from the relation
`vecF_m = q(vec v xx vev B)` we have `(4.0 hati + 3.0 hatj) xx 10^(-10) = 10^(-9) [ (v_x hati + v_y hatj) xx (4 xx 10^(-3) hatk) ] `
`(4y_y + 10^(-12) hati - 4 v_x xx 10^(-12) hatj )`
comparing the cofficient of `hati` and `hatj` we have
` 4 xx 10^(-10) = 4v_y xx 10^(-12)`
` therefore v_y = 10^2 m//s = 100 m//s ` and
` 3.0 xx 10^(-10) = -4v_x xx 10^(-12)`
` therefore v_x = -75 m//s therefore vecv = -75 hati + 100 hatj`