A particle carrying a charge `3 muC `is moving with velocity `vecv = (6hatj + 2hati)ms^(-1)` in a magnetic field `vecB = (2hati + 6hatj)wbm^(-2)`. Find the force acting on the particle.

Explanation

`q = 3 muC = 3 xx 10^(-6)C`
`vecv = (6hatj + 2hati) ms^(-1)`
`vecB = (2hati + 6hatj)ms^(-1)`
`vecF = ?`
`vecF = q(vecv xx vecB)`
`vecF = q[(6hatj + 2hati) xx (2hatj + 6hatj)]`
`vecF = q[(12hatj + hati + 36hatj xx hatj + 4hati xx hati + 12hatj xx hatj)]`
`because hati xx hati = hatj xx hatj = hatk xx hatk =0`
and `hatj xx hati = -hati xx hatj`
`therefore vecF = q[-12hati xx hatj + 0 + 0 + 12hati xx hatj]`
`rArr vecF = q (0) = 0`
`therefore F = 0`