# EMF find the electric field

## Homework Statement

The region is a circle with radius=a

## Homework Equations

Using Faraday's law to find E.

## The Attempt at a Solution

Dealing with the Left side of the second equation first
1.) Pull out the Partial/partial t because it is a constant in this equation
2.) Now I have B dot (n-hat) da
3.) Using the dot product I know that I have |B||da|cos(theta)
4.) the angle between them is zero so I have B*da
5.) I can pull B out and integrate over the area of the circle which gives me A=2(pi)(r)^2 =2(pi)(a)^2
6.) Now I have
-[2(pi)(a)^2 * Partial(B)/partial t] this is also equal to equation 1 our emf induced
7.) Taking the partial of B with respect to t gives me
-[2(pi)(a)^2 *
]

Now I deal with the right side of equation 2 which is equal to 7.)

[/B]
8.) I know that E is parallel to dl and that I can pull E out
9.) Now I integrate over dl which just gives me

E*2(pi)(r)= -[2(pi)(a)^2 *
]

of course excluding the B(x,y,t).

Then I divide by 2(pi)r)
Which will give me E if I did everything correctly

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## Answers and Replies

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kuruman
Homework Helper
Gold Member
5.) I can pull B out and integrate over the area of the circle ...
Is B constant over the surface area of the circle?

Yes

kuruman