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MHT CET 2020 (19 Oct, Shift 2) · Biot-Savart Law & Circular Coils

Biot-Savart Law & Circular Coils question from MHT CET 2020 (19 Oct, Shift 2)

Q84MHT CET 2020 · 19 OCT · SHIFT 2Medium

Biot-Savart Law & Circular Coils

An electron moves in a circular orbit with uniform speed vv. It produces a magnetic field BB at the centre of the circle. The radius of the circle is [ μ0=\mu_0 = permeability of free space, e=e = electronic charge]

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Answer: (a)

  1. I=eT=ev2πrI = \frac{e}{T} = \frac{ev}{2\pi r}, so B=μ0I2r=μ0ev4πr2B = \frac{\mu_0 I}{2r} = \frac{\mu_0 e v}{4\pi r^2}.
  2. r2=μ0ev4πB⇒r=(μ0ev4πB)1/2r^2 = \frac{\mu_0 e v}{4\pi B} \Rightarrow r = \left(\frac{\mu_0 e v}{4\pi B}\right)^{1/2}
  3. So the answer is (a) (μ0ev4πB)1/2\left(\frac{\mu_0 e v}{4\pi B}\right)^{1/2}.
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