A tightly wound long solenoid carries a current of $1.5$ A. An electron is executing uniform circular motion inside the solenoid with a time period of $75$ ns. The number of turns per metre in the solenoid is ...... [Take mass of electron $m_e=9 imes10^{-31}$ kg, charge of electron $|q_e|=1.6 imes10^{-19}$ C, $\mu_0=4\pi imes10^{-7}\,\frac N{A^2}$, $1 ext{ ns}=10^{-9}$ s]

Question

A tightly wound long solenoid carries a current of $1.5$ A. An electron is executing uniform circular motion inside the solenoid with a time period of $75$ ns. The number of turns per metre in the solenoid is ...... [Take mass of electron $m_e=9	imes10^{-31}$ kg, charge of electron $|q_e|=1.6	imes10^{-19}$ C, $\mu_0=4\pi	imes10^{-7}\,\frac N{A^2}$, $1	ext{ ns}=10^{-9}$ s]

Dr. Abubacker · Accepted Answer

[Solution by Dr. Abubacker] $T=\frac{2\pi m}{eB}\Rightarrow B=\frac{2\pi m}{eT}=\frac{2\pi	imes9	imes10^{-31}}{1.6	imes10^{-19}	imes75	imes10^{-9}}=4.71	imes10^{-4}$ T. $B=\mu_0nI\Rightarrow n=\frac{4.71	imes10^{-4}}{4\pi	imes10^{-7}	imes1.5}=250$ turns/m. Answer: 250.

Explanation

Reviewed by Dr. Abubacker

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