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Question
A long straight wire AB carries a current I. A particle (mass m and charge q) moves with a velocity `vec"v"`, parallel to the wire, at a distance d from it as shown in the figure. Obtain the expression for the force experienced by the particle and mention its directions.
Solution
Magnetic field induction at P due to current I in long straight wire AB is
`B = mu_0/(4pi) (2I)/d`
It acts perpendicular to the plane of the paper inward, represented by `hatn`.
Lorentz force acting on the particle at P can be given by
`vecF = q(vecv xx vecB) = e(vecv xx (mu_0. 2I)/(4pid)hatn)`
or `vecF = (mu_0Iev)/(2pid)(hatv xx hatn)`
∴ `F = (mu_0Iev)/(2pid)`
Acting in the plane of paper away from the wire.
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