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Question

A long solenoid has 100 turns/cm and carries current $$i$$. An electron moves within the solenoid in a circle of radius 2.30 cm perpendicular to the solenoid axis. The speed of the electron is 0.0460c (c = speed of light). Find the current $$i$$ in the solenoid.


Solution

The orbital radius for the electron is $$r=\dfrac{mv}{eB}=\dfrac{mv}{e\mu_{0}ni}$$ 

which we solve for $$i$$:
$$i=\dfrac{mv}{e\mu_{0}nr}=\dfrac{(9.11\times 10^{-31}\hspace{0.05cm}kg)(0.0460)(3\times 10^8\hspace{0.05cm}m/s)}{(1.60\times 10^{-19}\hspace{0.05cm}C)(4\pi \times 10^{-7}\hspace{0.05cm}T.m/A)(100/0.0100m)(2.30\times 10^{-2}\hspace{0.05cm}m)}=0.272\hspace{0.05cm}A$$

Physics

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