A test charge of `1.6 xx 10^-19` C is moving with velocity ` v = (2hati+3hatj) m/sec `in magnetic field `vec B = (2hati + 3hatj) Wb m^-2`. Find the force acting on the test charge.

Explanation

`vecv = (2 hati + 3hatj) ms^(-1)`
`vec(B) = (2hati + 3hatj) wb//m^(-2)`
`q = 1.6 xx 10^(-19) C`
`vecF = q(vecv xx vecB)`
`vecF = 1.6 xx 10^(-19)[(2hati + 3hatj) xx (2 hati xx 3 hatj)]`
`= 1.6 xx 10^(-19) [4hati xx hati xx 6hati xx hatj + 6hatj xx hati + 9hatj xx hatj xx j]`
`because hati xx hati = hatj xx hatj = 0 `
and `hati xx hatj = hatk` and `hatj xx hati = - hatk`
`therefore F = 1.6 xx 10^(-9)`
`[0 + 6 hatk - 6 hatk + 0]`
`F = 0`
As `F = 0` , so test charge is moving parallel to magnetic field.