## 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. What is the induced current in the bar when the terminal speed has been reached?

Solution

Verified(c) From equation (*), the induced emf when the terminal speed is reached is:

$\begin{gathered} \varepsilon = BLv_t\ \cos{\phi} \end{gathered}$

From Ohm’s law, the current in the circuit is given by:

$\begin{gathered} I = \dfrac{\varepsilon}{R} = \dfrac{BLv_t\ \cos{\phi}}{R} \end{gathered}$

Substituting for $v_t$ from part (b), we get:

$\begin{gathered} I = \dfrac{BL\ \cos{\phi}}{R}\ \dfrac{mgR\ \sin{\phi}}{L^2 B^2 \cos^2{\phi}}\\\\ \therefore \quad \large \boxed{I = \dfrac{mg\ \tan{\phi}}{LB}} \end{gathered}$

## Create an account to view solutions

## Create an account to view solutions

## Recommended textbook solutions

#### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

4th Edition•ISBN: 9780133942651 (4 more)Randall D. Knight#### Sears and Zemansky's University Physics

14th Edition•ISBN: 9780133969290Hugh D. Young, Roger A. Freedman#### Mathematical Methods in the Physical Sciences

3rd Edition•ISBN: 9780471198260Mary L. Boas#### Fundamentals of Physics

10th Edition•ISBN: 9781118230718 (5 more)David Halliday, Jearl Walker, Robert Resnick## More related questions

1/4

1/7