# Induced EMF Question: Calculate the Answer

• liamporter1702
In summary, the magnetic flux decreases at a rate of 0.2Wb/m^{2}/s around a 24mmx36mm wire loop in a magnetic field. The induced emf around the loop is 0.17mV.
liamporter1702

## 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

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!

jaytech said:
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.!

jaytech said:
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.

jaytech said:
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.

## 1. What is induced EMF?

Induced EMF (electromotive force) is the voltage generated in a conductor or circuit when it is exposed to a changing magnetic field.

## 2. How is induced EMF calculated?

Induced EMF can be calculated using Faraday's Law, which states that the induced EMF is equal to the rate of change of magnetic flux through a circuit. It can be expressed by the equation E = -N(dΦ/dt), where E is the induced EMF, N is the number of turns in the coil, and dΦ/dt is the rate of change of magnetic flux through the coil.

## 3. What is the unit of induced EMF?

The unit of induced EMF is volts (V) in the SI system of units.

## 4. Can induced EMF be negative?

Yes, induced EMF can be negative. This occurs when the magnetic flux through the circuit decreases, causing the direction of the induced current to be opposite to the direction of the original current.

## 5. What are some real-life applications of induced EMF?

Some real-life applications of induced EMF include generators, transformers, and induction cooktops. Induced EMF is also used in electromagnetic sensors, such as speed sensors in cars and magnetic strip readers in credit cards.

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