Answer to Question #175853 in Electric Circuits for Joshua Musyoki

Question

A conductor of length 𝐿 moves at a steady speed vat right angles to a uniform magnetic field of flux density 𝐵. Show that the e.m.f. 𝐸 across the ends of the conductor is given by the equation 𝐸 = 𝐵𝑙𝑣.

Answer 1

Explanations & Calculations

• Considering the definition of the induced electromotive force: Faraday's law of induction, this could be evaluated.

$\qquad\qquad \begin{aligned} \small E&=\small -\frac{d\phi}{dt}\\ &=\small -\frac{d(B\times A)}{dt}\\ &=\small- B\cdot\frac{dA}{dt}\\ &=\small -B\cdot\frac{d(L\times x)}{dt}\\ &=\small -BL\cdot\frac{dx}{dt}\\ &=\small -BL\cdot v\\ \\ \small E&=\small -BLv \end{aligned}$ : x= any arbitrary distance it travels along the given direction.

• The negative mark emphasizes that the induction is in the reversed direction.