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At a distance l from a uniformly charged...

At a distance l from a uniformly charged long wire, a charged particle is thrown radially outward with a velocity u in the direction perpendicular to the wire. When the particle reaches a distance 2l from the wire its speed is found to be `sqrt(2)u`. The magnitude of the velocity, when it is a distance 4l away from the wire, is (ignore gravity)

A

`sqrt3u`

B

2 u

C

`2sqrt2 u`

D

4 u

Text Solution

Verified by Experts

The correct Answer is:
A
Energy conservation at A and B
`qV_A +1/2 "mu"^2 =qV_B+1/2 xx 2"mu"^2 implies q[V_A-V_B]=1/2"mu"^2`
`qxxlamda/(2piepsilon_0) ln 2 =1/2"mu"^2`
Energy conservation at A and C
`q[V_A-V_C]+1/2"mu"^2 =1/2 "mv"^2=1/2"mv"^2`
`implies (qlamda)/(2pi epsilon_0) ln 4 +1/2 "mu"^2 =1/2"mv^2`
`(2qlamda)/(2piepsilon_0)ln2 +1/2"mu"^2=1/2"mv"^2`
`implies 3/2u^2=1/2v^2 implies v=sqrt3u`
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