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A long straight wire AB carries a curren...

A long straight wire AB carries a current of `4A`. A proton P travels at `4xx10^6ms^-1` parallel to the wire, `0*2m` from it and in a direction opposite to the current as shown in figure. Calculate the force which the magnetic field of current exerts on the proton. Also specify the direction of the force.

Text Solution

Verified by Experts

Here, `I=4A`, `v=4xx10^6ms^-1`,
`r=0*2m`.
Magnetic field induction at P is
`B=(mu_0)/(4pi)(2I)/(r)=(10^-7xx2xx4)/(0*2)=4xx10^-6T`
The direction of `vecB`, according to Right Hand Thumb rule, is perpendicular to the plane of paper directed inwards.
Since proton is moving in opposite direction to the current carrying straight wire, hence the proton is moving perpendicular to the direction of mangetic field due to current through straight wire. The force on moving proton of charge q due to magnetic field is
`F=qvBsin 90^@`
`=(1*6xx10^(-19))xx(4xx10^6)xx(4xx10^-6)`
`=2*56xx10^(-18)N`
According to Fleming's Left Hand Rule, the force acts in the plane of paper towards right.
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