Electromagnetic Induction in the Earths Field

[pobatso]

Hi all, brand new to these forums but help you can give me some guidance with some summer exam revision!
Heres a fairly simple one I can't see through for some reason, using EMF = B.u.l etc:

1. A copper disc, 250mm in diameter, is reotated at 300 rpm about a horizontal axis through its centre and perpendicular to its plane. If the axis points magnetic north and south, calculate the emf between the circumference of the disc and the axis. Assume the horizontal comp. of the Earth's mag field to be 18 uT
2. EMF = B.u.L
3. B = Stated, u = speed of the circumference of the ring, so (pi x D)(revs. per sec), L = Circumference (0.7854m) Ans= 5.6x10^-5, wrong answer :(

Im pretty sure its simple, but I think I am confusing some of the figures. Cheers!

 

[mark726]

Hi there,

Thanks for reaching out to the forum for help with your summer exam revision! I'm happy to assist you with this problem.

Let's break down the problem and see where you may have gone wrong in your calculations.

1. First, let's identify the given information:
- Copper disc diameter = 250mm = 0.25m
- Rotation speed = 300 rpm (revolutions per minute)
- Earth's magnetic field horizontal component = 18 uT (microtesla)

2. Now, let's identify the formula we will use:
EMF = B.u.L

3. We need to find the value for B (magnetic field strength), u (speed of the circumference of the ring), and L (circumference).

B = 18 uT = 18 x 10^-6 T (since 1 uT = 10^-6 T)

4. To find u, we need to convert the rotation speed from rpm to revs. per second:
300 rpm = 300/60 = 5 revs. per second

Now, we can calculate the speed of the circumference of the ring:
u = (pi x D)(revs. per sec) = (pi x 0.25m)(5 revs. per sec) = 0.7854 x 5 = 3.927 m/s

5. Finally, we can calculate the circumference of the disc:
L = pi x diameter = pi x 0.25m = 0.7854m

6. Now, we can plug in the values into the formula:
EMF = (18 x 10^-6 T) x (3.927 m/s) x (0.7854m) = 5.5 x 10^-5 V

Therefore, the EMF between the circumference of the disc and the axis is 5.5 x 10^-5 V.

I hope this helps clarify any confusion and helps you with your revision. Good luck on your exams!