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Consider a Long, Straight Wire of Cross-sectional Area a Carrying a Current I. Let There Be N Free Electrons per Unit Volume. - Physics

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Question

Consider a long, straight wire of cross-sectional area A carrying a current i. Let there be n free electrons per unit volume. An observer places himself on a trolley moving in the direction opposite to the current with a speed  \[v = \frac{i}{\text{nAe}}\] and separation from the wire by a distance r. The magnetic field seen by the observer is very nearly  

Options

  • \[\frac{\mu_0 i}{2\pi r}\]
  • zero

  • \[\frac{\mu_0 i}{\pi r}\]
  • \[\frac{2 \mu_0 i}{\pi r}\]
MCQ

Solution

Magnetic field will be independent of the motion of the observer because the velocity with which the observer is moving is comparable to drift velocity of electron which is very small as compared to the speed of flow of current from one end of wire to other end. So it can be neglected  and hence, magnetic field due to the wire w.r.t the observer will be

B = \[\frac{\mu_o i}{2\pi r}\]

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Motion in a Magnetic Field
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Chapter 13: Magnetic Field due to a Current - MCQ [Page 249]

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HC Verma Concepts of Physics Vol. 2 [English] Class 11 and 12
Chapter 13 Magnetic Field due to a Current
MCQ | Q 12 | Page 249

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