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A long straight wire AB carries a curren...

A long straight wire AB carries a current I. A proton P travels with a speed v, parallel to the wire , at a distance d from it in a direction opposite to the current as shown in figure what is the force experienced by the proton and what is its direction?

Text Solution

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Magnetic field due to current carrying wire is perpendicular to plane of paper - downward.

i.e `vecB = - (mu_(0)I)/(2 pi f) hatv`
Force `vecF = q ( vecv xx vecB) = e [(-v hatj) xx ((mu_(0)I)/(2 pi d) hat v)]`
` = (mu_(0)ev I)/(2 pi d) hati `
That is the magnetic force has magnitude `(mu_(0)e v I)/(2 pi d) `
and is directed along `+ `ve X - axis i.e in the plane of paper perpendicular to direction of `vecv` and to the right.
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