Induced emf:

$\overline{){\mathbf{\epsilon}}{\mathbf{=}}{\mathit{v}}{\mathbf{B}}{\mathbf{L}}}$

Ohm's law:

$\overline{){\mathit{i}}{\mathbf{=}}\frac{\mathbf{V}}{\mathbf{R}}}$

Magnetic force on a current-carrying conductor:

$\overline{){{\mathbf{F}}}_{{\mathbf{B}}}{\mathbf{=}}{\mathbf{B}}{\mathbf{i}}{\mathbf{Lsin\theta}}}$

Newton's second law:

$\overline{){\mathbf{\Sigma}}{\mathbf{F}}{\mathbf{=}}{\mathbf{m}}{\mathbf{a}}}$

Net emf, ε_{net} = ε_{applied} + ε_{induced} = **V + vBL**

This problem explores how a current-carrying wire can be accelerated by a magnetic field. You will use the ideas of magnetic flux and the EMF due to the change of flux through a loop. Note that there is an involved follow-up part that will be shown once you have found the answer to Part B.

A) What is the acceleration *a*_{r}(*t*) of the rod? Take *m* to be the mass of the rod.

Express your answer as a function of *V*, *B*, the velocity of the rod *v*_{r}(*t*), *L*, *R*, and the mass of the rod *m*.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Motional EMF concept. You can view video lessons to learn Motional EMF. Or if you need more Motional EMF practice, you can also practice Motional EMF practice problems.