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In a certain region of space a uniform a...

In a certain region of space a uniform and constant electric field and a magnetic field parallel to each other are present. A proton is fired from a point A in the field with speed `V=4xx10^(4)m//s` at an angle of `alpha` with the field direction. The proton reaches a point B in the field where its velocity makes an angle `beta` with the field direction. If `(sinalpha)/(sinbeta)=sqrt3.` Find the electric potential difference between the points A and B. Take mp (mass of proton) `=1.6xx10^(-27)`kg and e (magnitude of electronic charge) `=1.6xx10^(-19)`C.

A

`16 V`

B

`16//3 V`

C

`90 V`

D

`30 V`

Text Solution

Verified by Experts

Work done by magnetic force is zero
so from work energy theorem
`(1)/(2)m_(p)v_(B)^(2)=(1)/(2)m_(p)v_(A)^(2)+qDeltaV`
and simultaneously there is no change of velocity component along the direction of perpendicular to electric and magnetic field.
`v_(A)sinalpha=v_(B)sinbeta`
After solving `Deltav=16` Volt
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