An electron enters an electric field having intensity `vecE=3hati+6hatj+2hatkV.m^(-1)` and a magnetic field having induction `vecB=2hati+3hatjT` with a velocity `vecv=2hati+3hatjm.s^(-1)`. The magnitude of the force acting on the electron is (Given `e=-1.6xx10^(-19)C`)

Options

A. `2.02xx10^(-18)N`
B. `5.16xx10^(-16)N`
C. `3.72xx10^(-17)N`
D. `4.41xx10^(-18)N`

Explanation

Force on the electron,
`vecF=e(vecE+vecvxxvecB)`
Now, `vecvxxvecB=|{:(hati,hatj,hatk),(2,3,0),(2,3,0):}|=vec0`
`:.vecF=-1.6xx10^(-19)(3hati+6hatj+2hatk+vec0)`
`:.` Magnitude of force `=1.6xx10^(-19)sqrt(3^(2)+6^(2)+2^(2))`
`=1.12xx10^(-18)N`
None of the options is correct.