A particle carrying a charge `5 mu C` is moving with a velocity `vecv = ( 4 hati + 3 hatk) ms ^(-1)` in a magnetic field `vec B =( 3 hatk + 4 hati) W bm^(-2).` Calculate the force acting on the particle.

Explanation

`q = 5 muC = 5 xx 10^(-6)` C
`vecv = (4hati + 3hatk) ms^(-1)`
`vecB = (3hatk + 4hati) wbm^(-2)`
Force = F = ?
`vecF = q(vecv xx vecB)`
` = 5 xx 10^(-6) [(4hati +3hatk) xx (3hatk + 4hati)]`
` = 5 xx 10^(-6) [12hati xx hatk + 16hati xx hati xx +9hatk xx hatk + 12hatk xx hati]`
`because hati xx hati = hatj xx hatj = hatk xx hatk = 0`
and `hatk xx hati = -hati xx hatk`
`therefore vecF = 5 xx 10^(-6) [12hati xx hatk + 0 + 0 -12hati xx hatk]`
`vecF = 0`