Calculating Induced EMF: 50 cm^2 to .005 M^2

[Gemy4]

Homework Statement

A flat coil of wire consisting of 20 turns, each with an area of 50 cm^2 is positioned so that the normal to its plane is at the angle of 30 degrees to a uniform magnetic field that increases its magnitude at a constant rate from 2.0T to 8.0T in 2.0 s.

Homework Equations

Induced EMF(E)= -rate of change of magnetic flux/ change of time

The Attempt at a Solution

Induced EMF(E)= rate of change of magnetic flux/ change of time
or = (N)(Change of B)(A)(COS Theta)/ Change of Time

N=20
A= 50 cm^2
Change of Time= 2.0 S
COS 30 degrees= .87
Change of B= 8.0T-2.0T=6.0T

The solution as posted by the teacher was,

Induced EMF(E)= (20)(6.0T)(.005M^2)(.87)/ 2 s
= .260 V

I do not understand how 50 cm^2 becomes .005M^2
also what happened to the negative sign?

Thank you!

 

[Gemy4]

anyone?

 

[Lunat1c]

The negative sign is only introduced to show that the emf is in the opposite direction of the change in flux producing it (check out Lenz's Law).

Now, to convert 50 cm^2 you could go about it this way:

1cm^2 = 0.0001m^2
50cm^2 = x m^2

x = 50 \times 0.0001 / 1 = 0.005m^2

 

[Gemy4]

Thank you!

 

[Lunat1c]

No problem. Make sure you're familiar with unit conversions, you'll tend to encounter these a lot as you go along.