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A particlewith specific charge q//m is located inside a roundsolenoid at a distance r fromits axis. With the currentswichted into the winding, the magnetic induction of the field generated by thesolenoid amountsto B. Find thevelocity of the particleand the curvatureradius of itstrajectory,n assumingthat duringthe increase of currentflowingin the solenoid the particle shifts by a negligible distance. |
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Answer» Solution :When the magnetic field is beingset up in the solenoid, and ELECTRIC field will be induced in it, this will acceleratethe CHARGED paritcle. If `B` is the rate, at which the matgnetic field is increasing, then. `pi r^(2) dotB = 2pi r E` or `E = (1)/(2) r dotB` Thus, `m (dv)/(DT) = (1)/(2) r dotB q`, or `v = (qBr)/(2m)`, After the field is set up, the parcticlewill execute a circularmotionof radius`rho`, where `MV = B q rho`, or `rho = (1)/(2) r` |
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