A proton of velocity `(3hati+2hatj)ms^(-1)` enters a field of magnetic induction `(2hatj+3hatk) T`, the acceleration produced in the proton in `ms^(-2) ` is (specific charge of proton = `0.96xx10^(8)C-kg^(-1)`)

Options

A. `2.8xx10^(8)(2hati-3hatj)`
B. `2.88xx10^(8)(2hati-3hatj+2hatk)`
C. `2.8xx10^(8)(2hati-3hatk)`
D. `2.88xx10^(8)(hati-3hatj+2hatk)`

Answer

B

Explanation

Given `overlineV=(3hati+2hatj)ms^(-1), overlineB=(2hatj+3hatk)T,`
`q/m=0.96xx108 Ckg^(-1)`
Force acting on the proton overlineF=q(overlineVxxoverlineB)`
overlineVxxoverlineB=|(hati,hatj,hatk),(3,2,0),(0,2,3)|`
`=hati(6)-hatj(9)+hatk(6)`
`F=q(6hati-9hatj+6hatk)`
`moverlinea=q(6hati-9hatj+6hatk)`
`overlinea" "q/m(6hati-9hatj+6hatk)`
`=0.96xx10^(8)xx3(2hati-3hatj+2hatk)`
`=2.88xx10^(8)(2hati-3hatj+2hatk)`