# Induced EMF Question

## Homework Statement

A rectangular wire loop, 24mm by 36mm, is placed in a magnetic field. The flux density perpendicular to the loop is decreasing in magnitude at a rate of 0.2Wb/$m^{2}$/s. Calculate the induced emf around the loop.

## Homework Equations

The problem is I don't know which equation applies to this question. I know that 0.2Wb/$m^{2}$/s = $\frac{d\phi}{dt}$ but as far as I was concerned from what I have read so far is that you would need to know the number of loops to get the answer to this question.

## The Attempt at a Solution

I know that the answer is 0.17mV. I managed to get this answer by multiplying the dimensions together 24mm x 36mm = 8.64x$10^{-4}$ then multiply this by 0.2. But I don't understand why this this is the method, if someone could explain this for me I would greatly appreciate it

## Answers and Replies

Let's look at the equation in question: $\int$$\vec{B}$$\cdot$d$\vec{A}$ = - N*d$\phi$/dt

Since you're examining magnitudes, let's forget the minus sign. You have B, and the problem states there is one rectangular loop, so you know N. The induced EMF is defined by d$\phi$/dt, so all that's missing is ∫dA. That's just A, which you calculated.

That's why the given B multiplied by the A you calculated gives your answer, and why N = 1.

1 person
As always, it's best to start with the general form of the applicable physical principle. In this case, what is the relationship between induced emf and magnetic flux?

1 person
Ah I see where I have gone wrong! Was just a matter of reading the question properly Thanks a lot guys!

rude man
Homework Helper
Gold Member
Let's look at the equation in question: $\int$$\vec{B}$$\cdot$d$\vec{A}$ = - N*d$\phi$/dt

?? Don't look at it too long ....

Edit: Oops! I forgot the d/dt on the L.H.S.!!

rude man
Homework Helper
Gold Member
Edit: Oops! I forgot the d/dt on the L.H.S.!!

Also the N ...

B is a function of N, so it isn't necessary to include on the L.H.S. It is implied.

rude man
Homework Helper
Gold Member
B is a function of N, so it isn't necessary to include on the L.H.S. It is implied.

Then it's implied in ø on the right-hand side as well, so you'd have to get rid of it there.

N needs to be on the left and right.
The relation is ∫B.dA = ø, and emf = - N dø/dt.