# Anyone know anything about induced electric fields?

• shikagami
In summary, the magnetic field in a long solenoid is equal to the time rate of change of the magnetic flux through the loop. The induced emf around a loop is equal to the total change in flux divided by the time this change took. The equation for the magnetic field inside a long solenoid in terms of the number of turns of wire per unit lenght. This should be in your notes or book somewhere. The equation relating the induced emf in a circuit in terms of the rate of change of flux: \mathcal{E}_{induced}=-\frac{\Delta \Phi_B}{\Delta t}
shikagami
Here's the problem: Can someone help me start it off?

A long straight solenoid of cross-sectional area 6 cm^2 is wound with ten turns of wire per centimeter, and the windings carry a current of 0.25 A. A secondary winding of two turns encircles the solenoid. When the primary circuit is opened, the magnetic field of the solenoid becomes zero in 0.05s. What is the average induced emf in the secondary?

The EMF induced around a loop is equal to the time rate of change of the magnetic flus through the loop. So the average induced EMF would be equal to the total change in flux divided by the time this change took. The flux is just the integral of B.dA over the surface bounded by the loop.

To do this problem, you will need...

1) ...to understand the concept of the magnetic flux through a surface. If you haven't mastered this, go back to studying your notes or book.

2) The equation for the magnetic field inside a long solenoid in terms of the number of turns of wire per unit lenght. This should be in your notes or book somewhere.

3) The equation relating the induced emf in a circuit in terms of the rate of change of flux:

$$\mathcal{E}_{induced}=-\frac{\Delta \Phi_B}{\Delta t}$$

This equation is saying that for each Tesla per second by which the flux through the loop making the circuit changes , there is an induced emf of 1 Volt.

mmmh.

Post your progress if you need further assistance.

can i use this equation to solve for the magnetic field?

B=MIn

If my M you mean $$\mu_0$$, then yes, this is exactly the expression of the magnitude of B inside a long soleoid.

how do i figure out what n is if I don't have length. Should I use the area to find the length which is equal to 2r?

well... i got a magnetic field of 1.14 x 10^-6 T

shikagami said:
how do i figure out what n is if I don't have length.
n is given to you in the problem: 10 turns per centimeters = 1000 turns per meter.

shikagami said:
Should I use the area to find the length which is equal to 2r?

Here, "lenght" applies to the length of the solenoid itself, not of the wire composing it.

So 1000 turns/m does not mean that the people who constructed the soleoid made 1000 turns out of 1 meter of wire. It means that for each meter of the height of the solenoid (considered as a big cylinder), there is 1000 turns of wire.

ohhh ok. here's what i got so far 3.15 x 10 ^ -4 T for the magnetic field.

Yes, good! Actually the exact value is $\pi \times 10^{-4} T$ .

yay... so I use the emf equation and get -3.78 x 10 ^-6 V. does that sound good?

I don't think. The next step after finding the field is finding the magnetic flux through the secondary winding. (We assume that the secondary winding has the same radius as the primary one)

How did you go about that?

(sorry for the delay, I had to kill the nastiest spider)

so i multiply my emf by 2 which gives me -7.56 x 10 ^ -6 V

?!

What value did you get for $\Phi_B$ through the secondary winding?

umm... 3.78 x 10^-7 V

Volts!? I think you might be confusing emf and magnetic flux! Go look up the definition of magnetic flux through a surface.

(going to sleep now, good luck)

## 1. What is an induced electric field?

An induced electric field is a type of electric field that is created when a changing magnetic field passes through a conductor, such as a wire. This changing magnetic field induces an electric field in the conductor, which can cause charges to flow and create an electric current.

## 2. How is an induced electric field different from a static electric field?

A static electric field is a constant electric field that does not change over time. An induced electric field, on the other hand, is created by a changing magnetic field and is not a constant field. It only exists while the changing magnetic field is present.

## 3. What are some examples of induced electric fields?

An example of an induced electric field is the electric field created by a generator. The generator uses a changing magnetic field to induce an electric field in a wire, which then produces an electric current. Another example is the electric field created by a transformer, which uses a varying magnetic field to induce an electric field and transfer energy between two circuits.

## 4. How can we measure and detect induced electric fields?

Induced electric fields can be measured and detected using various instruments, such as voltmeters and oscilloscopes. These instruments can detect the presence of an electric field and measure its strength and direction. Another method is to use a Faraday cage, which can shield an object from external electric fields, allowing for the measurement of induced electric fields in a controlled environment.

## 5. What are the applications of induced electric fields?

Induced electric fields have many practical applications, including generators, transformers, and electric motors. They are also used in technologies such as wireless power transfer, magnetic levitation, and induction heating. In addition, induced electric fields play a crucial role in electromagnetic induction, a fundamental principle in physics and engineering.

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