# A man moves his head back and forth between the poles of a powerful magnet. He moves...

## Question:

A man moves his head back and forth between the poles of a powerful magnet. He moves perpendicular to the field at a maximum speed of 150 m/s. If he can taste on his tongue, an electric field of 10 V/m, how powerful must the magnetic field be so that he may taste it?

## Motional Electromotive force:

The motional electromotive force is the induced electromotive force by a moving conductor. The induced electromotive force is a potential difference and have the units of volts. The motional electromotive force works at right angles and is proportional to the velocity and length of the conductor.

The magnetic field is {eq}0.067 T {/eq}

Solution:

The motional electromotive force is

{eq}\epsilon=vBL {/eq}

{eq}\frac{\epsilon}{L}=vB {/eq}

since the units of {eq}\frac{\epsilon}{L}=\frac{[V]}{[m]} {/eq} is the units of the electric field

finding the magnetic field

{eq}B=\frac{\epsilon}{Lv} {/eq}

{eq}B=(\frac{\epsilon}{L})v {/eq}

{eq}B=\frac{10 \frac{V}{m}}{150 \frac{m}{s}} {/eq}

{eq}B=0.067 T {/eq}