An ideal long solenoid of radius has turns per metre and carries

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Magnetostatics · Electromagnetic induction and alternating-current circuits

The Boundary-Value Problem, Ch The vector potential and the magnetostatic boundary-value problem

Problem

An ideal long solenoid of radius a=1.5 cma = 1.5\,\mathrm{cm} has n=6.0×103n = 6.0\times10^3 turns per metre and carries I=12 AI = 12\,\mathrm{A}. An alpha particle (charge q=2eq = 2e, mass mq=6.645×10−27 kgm_q = 6.645\times10^{-27}\,\mathrm{kg}) sits at rest inside the winding, at radius s=1.0 cms = 1.0\,\mathrm{cm} from the axis, where B≠0\mathbf{B}\ne0. The current is switched off quasistatically (slowly enough that Ampere's law still fixes the instantaneous B\mathbf{B}) but in a time short compared with the particle's cyclotron period 2πmq/qB2\pi m_q/qB, so that the particle drifts a negligible distance and the magnetic force on it during switch-off can be neglected. ((a)) Find BB inside the solenoid and AϕA_\phi at s=1.0 cms = 1.0\,\mathrm{cm} before switch-off. ((b)) Find the speed the alpha particle has immediately after the current is switched off. ((c)) If the particle could be placed at any radius, inside or outside the winding, where would the kick be largest? Find that largest speed.

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