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.