Verified Solution • 2025–26 Session moderate

QPages 249-253: Q58: HC Verma: Concepts of Physics - Volume 2 Magnetic Field Due to a Current Pages 249-253: Q58 Solution: A tightly-wound, long solenoid carries a current of 2.00 A. An…

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−11.00 \times 10^8 \text{ rev s}^{-1}. Find the number of turns per metre in the solenoid.

Step-by-Step Verified Solution

**Answer:** n=2.84×105n = 2.84 \times 10^5 turns/m. **Step-by-Step Explanation:** f=1×108f = 1 \times 10^8 rev/s, i=2i = 2 A. The electron's cyclotron frequency: f=eB2πmf = \frac{eB}{2\pi m}. B=2πmfe=2π×9.1×10−31×1081.6×10−19=3.57×10−3B = \frac{2\pi m f}{e} = \frac{2\pi \times 9.1 \times 10^{-31} \times 10^8}{1.6 \times 10^{-19}} = 3.57 \times 10^{-3} T. n=Bμ0i=3.57×10−34π×10−7×2=1420n = \frac{B}{\mu_0 i} = \frac{3.57 \times 10^{-3}}{4\pi \times 10^{-7} \times 2} = 1420 turns/m.

All Questions in this Chapter

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