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A long straight wire XY carries a curren...

A long straight wire XY carries a current of 2 amperes. A proton P travels at `5 xx 10^(-6)ms^(-1)` parallel to the wire as shown in the diagram, `0*2` m away from it. Find out the magnitude and direction of force which magnetic field exerts on the proton.

Text Solution

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`I =2A`
Velocity of proton ` = v = 5 xx 10^(-6)ms^(-1)`
Charge on the proton ` = q = 1*6 xx 10^(-19)C`
`r = 0*2` m
Let B = Magnetic field due to long straight wire at the site of proton
and `B =(mu_(0))/(4pi) (2I)/(r)`
`B = 10^(-7) xx (2xx 2)/(0*2)`
`B = 2 xx 10^(-6)T`
By right hand thumb rule, we come to know that magnetic field is perpendicular to the plane paper and in inward direction.
`rArr` Angle between velocity vector `vecv` and magnetic field
`F = Bq vecv sin theta`
`F = 2 xx 10^(-6) xx 1*6 xx 10^(-19 ) xx 5 xx 10^(-6) xx sin 90`
`F = 16 xx 10^(-31)` N
`F = 1*6 xx 10^(-30)` N
By Fleming.s left hand rule this force acts towards the wire XY.
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