A tightly-wound, long solenoid carries a current of 2.00 A. An electron is found to execute a uniform circular motion inside the solenoid with a frequency of 1.00 × 10⁸ rev/s. Find the number of turns per metre in the solenoid.
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Question

A tightly-wound, long solenoid carries a current of 2.00 A. An electron is found to execute a uniform circular motion inside the solenoid with a frequency of 1.00 × 10⁸ rev/s. Find the number of turns per metre in the solenoid.

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G1 Physics · Accepted Answer

Cyclotron frequency of an electron is f=eB/(2πm). Inside a long solenoid B=μ₀ni. Therefore n=2πmf/(eμ₀i)≈1.42×10³ turns/m. Hence D.