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A particle of specific charge q/m=pi C//...

A particle of specific charge `q/m=pi C//kg` is projected from the origin towards positive `x`-axis with a velocity of `10 m//s ` in a uniform magnetic field `vec(B)=-2hatk T`. The velocity `vec(v)` of particle after time `t=1/12 s` will be (in `m//s`)

A

`5[hati+sqrt(3)hatj]`

B

`5[sqrt(3)hati+hatj]`

C

`5[sqrt(3)hati-hatj]`

D

`5[hati+hatj]`

Text Solution

Verified by Experts

The correct Answer is:
B
Time period `T=(2pim)/(qB)`
`T=(2pi)/(pixx2)=1s`
Thus particle will beat point `P` after `t=1/12 s`.

`vec(v) = 10[cos30hati+sin30hatj]`
`vec(v)=10[(sqrt(3))/2hati+1/2hatj]=5[sqrt(3) hati+hatj] m//s`
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Knowledge Check

  • A particle of specific charge q//m = (pi) C//kg is projected from the origin towards positive x-axis with a velocity of 10 m//s in a uniform magnetic field vec(B) = -2 hat K Tesla. The velocity vec V of the particle after time t =1//6 s will be

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