E.m.f. induced in straight conductor

eqn 8

The diagram shows a straight conductor of length l moving with constant velocity v through a uniform magnetic field directed into the paper. The conductor is moving perpendicularly to the magnetic field.

Steps for electromagnetic induction:

  • Electrons in the conductor will experience a force of magnitude FB=qvB downwards. (Use Fleming’s Left Hand Rule)
  • Hence, free electrons will move to the lower end causing a net negative charge there and a net positive charge at the upper end.
  • An electric field is being set up within the conductor. The charges at the ends will build up until the downward magnetic force on the electrons is balanced by the upward electric force $F_{E} = qE$.
  • At equilibrium, the charges stop flowing. Hence,
    $$\begin{aligned} F_{B} &= F_{E} \\ qvB &= qE \\ E &= vB \end{aligned}$$

Since the electric field is constant, the potential difference set up across the ends is given by $\Delta V = El = Blv$.

Easy way of determining direction of induced e.m.f when a conductor moves in a magnetic field:

Fleming’s Right-Hand Rule


Diagram by Douglas Morrison DougM. Link: http://en.wikipedia.org/wiki/File:RightHandOutline.png. Distributed under under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.

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