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A charged particle carrying charge 1 mu ...

A charged particle carrying charge `1 mu C` is moving with velocity `(2 hati + 3hati + 4hatk) ms^(-1)`. If an external magnetic field of `(5 hati + 3hatj - 6hatk) xx 10^(-3)T` exists in the region where the particle is moving then the force on the particle is `vecF xx 10^(-9)N`. The vector `vecF` is :

A

`-0.30 hati +0.32 hatj - 0.09 hatk `

B

`-30hati +32hatj - 9hatk`

C

`-300hati +320hatj - 90hatk`

D

`-3.0hati +3.2hatij - 0.9hatk`

Text Solution

Verified by Experts

The correct Answer is:
B
`vecF = 9 (vecV xxvecB)` (force on charge particle moving in magnetic field)
`vecVxxvecB=(2hati+3hatj+4hatk)xx(5hati+3hatj-6hatk)xx10^(-3)`
`=((hati,hatj,hatj),(2,3,4),(5,3,-6))xx10^(-3)`
`=[hati[-18-12]-hatj[-12 -20]+hatk[6-15] xx10^(-3)`
`=[hati[-30]+hatj[32]+hatk[-9]]xx10^(-3)`
Force `=10^(-6)[-30hati+32hatj-9hatk]xx10^(-3)`
`=10^(-9) [-30 hati+32hatj-9hatk]`
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