# Electricity and Magnetism problem

1. Mar 6, 2004

### retupmoc

Not even sure where to begin with this question:

Estimate the magnitude of the potential difference produced by the motion of a conductor in the earths magnetic field for which B is 4.3x10^-5T and the angle of dip (the angle it makes with the horizontal) is 60 degrees. Take as an example a car bumper of length 1.5m travelling at 100kmh-1

Another question which seems so straight forward, i attempted i couldnt get the correct answer can you point me out where im going wrong.

A closely wound rectangular coil of 50 turns has dimensions 12cmx25cm. The plane of the coil is rotated from a position where it makes an angle of 45degrees with a magnetic field 2T to a position perpendicular to the field in a time of 0.1s. What is the average EMF induced in the coil?

i made a couple assumptions which im not sure are correct
1. i assumed the initial angle of 45 degrees was between the area vector normal to the plane of the coil to the direction of B.
2. that the angle through which the coil moved in 0.1s was 45degrees and not 315degrees as the question is unclear on this.

Heres what i did

found the area to be 0.0375m^2
then used the equation theta=w0t+0.5(alpha)t^2

assuming no angular acceleration as weve only been dealing with constant angular motion with ssimple ac generators and using theta=pi/4 radians i get w=7.85 rad s-1.

Then got E = wNBAsinwt which i thinks right. i then worked out E(max) and divided the answer by SQRT(2) assuming the root mean square emf by average EMF. the answer should be 8.787V but im almost double. Can you see where im going wrong

help would be much appreciated thanks

retupmoc

2. Mar 7, 2004

### Staff: Mentor

Start by figuring the direction of the magnetic force on the charge carriers in the bumper.
$$\vec{F} = q \vec{v} \times \vec{B}$$
Only the component along the length of the bumper (which is horizontal) contributes to the emf.
Looks good to me.
First, that area is wrong I think. More importantly, I think your approach is more complicated than needed. To find the average emf just find the change in flux divided by the time.