## Related questions with answers

A metal bar with length $L$, mass $m$, and resistance $R$ is placed on frictionless metal rails that are inclined at an angle $\phi$ above the horizontal. The rails have negligible resistance. A uniform magnetic field of magnitude $B$ is directed downward as shown in Fig. we saw earlier. The bar is released from rest and slides down the rails. After the terminal speed has been reached, at what rate is electrical energy being converted to thermal energy in the resistance of the bar?

Solution

Verified(d) We simply substitute for $I$ form part (c) and $R$ into equation (4), so we get the rate at which the electrical energy is converted into thermal energy in the bar:

$\begin{gathered} P_e = I^2 R = \left( \dfrac{mg\ \tan{\phi}}{LB}\right)^2\ R\\\\ \therefore \quad \large \boxed{P_e = \dfrac{m^2g^2R\tan^2{\phi}}{L^2 B^2}} \end{gathered}$

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