In Figure , a metal rod is forced to move with constant velocity $$\overrightarrow {v}$$ along two parallel metal rails, connected with a strip of metal at one end. A magnetic field of magnitude B = 0.350 T points out of the page.
(a) If the rails are separated by L = 25.0 cm and the speed of the rod is 55.0 cm/s, what emf is generated?
(b) If the rod has a resistance of $$18.0\Omega $$ and the rails and connector have negligible resistance, what is the current in the rod?
(c) At what rate is energy being transferred to thermal energy?
(a) Equation $$\mathscr{E}=\dfrac{d\Phi
_B}{dt}=\dfrac{d}{dt}BLx=BL\dfrac{dx}{dt}=BLv$$ leads to
$$\varepsilon=B L v=(0.350
\mathrm{T})(0.250 \mathrm{m})(0.55 \mathrm{m} / \mathrm{s})=0.0481 \mathrm{V}$$
(b) By Ohm's law, the induced current is
$$i=0.0481 \mathrm{V} / 18.0
\Omega=0.00267 \mathrm{A}$$
By Lenz's law, the current is clockwise in Figure.
(c) Equation $$P=i^2R\text{ (resistive dissipation) }$$ leads to $$P=i^{2}
R=0.000129 \mathrm{W}$$