EMF on a rod on rails (v = 6 m/s)

Problem

A rod of length $\ell = 25 \ \mathrm{cm}$ slides without friction on two parallel rails at $v = 6{,}0 \ \mathrm{m/s}$, in a field $B = 0{,}40 \ \mathrm{T}$ perpendicular to the plane of the rails. The rails are closed by a resistor $R = 1{,}5 \ \mathrm{\Omega}$. Calculate the induced EMF and the current.

Conducting rod sliding on rails in a field pointing out of the plane.

Solution

Motional EMF. As it moves, the rod increases the area of the circuit, and therefore the linked flux. The induced EMF is: $\mathcal{E} = B \ell v = 0{,}40 \cdot 0{,}25 \cdot 6{,}0 = \ev{0{,}60 \ \mathrm{V}}$

Current. The circuit is closed only by the resistor $R$; by Ohm’s law: $i = \frac{\mathcal{E}}{R} = \frac{0{,}60}{1{,}5} = \ev{0{,}40 \ \mathrm{A}}$

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Topics: Induzione elettromagnetica Concepts: Legge di Faraday-Neumann-Lenz · Forza elettromotrice · Legge di Ohm Skills: Bilancio di flusso