# Challenging question about electromagnetic induction

• Naman Singh
In summary: The electric field lines in the region of interest are concentric circles. What does this suggest about ##\int \vec E \cdot d\vec l## along segment PQ? What about along segment RS or any radial line segment?The electric field lines in the region of interest are concentric circles. What does this suggest about ##\int \vec E \cdot d\vec l## along segment PQ? What about along segment RS or any radial line segment?In summary, the author is trying to solve for the electric field induced in the side PQ of a magnetic field. By symmetry, they can assume that the electric field lines are concentric circles. They can
Naman Singh

## Homework Statement

I have been stuck on this for weeks

∫E.dl = -dφ/dt

## The Attempt at a Solution

Total EMF (V) = -dφ/dt (Where φ is the magnetic flux through the loop)
⇒V = -A(dB/dt) (Since Area remains constant)
⇒V = -Ax (x=dB/dt)
⇒V = -2xl^2
I do not know how to proceed.

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I'm no expert on this, and I can't find an online reference to support this idea, but maybe you can assume that as the field strength changes lines of flux move radially. That would show where no emf is produced. You can then cut the triangle in a certain way to figure out the remaining two emfs.

I guess that the phrase "emf induced in the side PQ" means the magnitude of the integral ∫E.dl, where the integral is taken along the side PQ and E is the induced electric field.

By symmetry, what can you say about the shape of the induced electric field lines?
Can you use ##\oint##E.dl = -dφ/dt to determine the magnitude of E at any point within the magnetic field region?

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I agree with @TSny's assessment. I would also recommend that you write the electric field vector in Cartesian coordinates after you find it and before you do the line integrals.

In the diagram, PQ >> PR yet it says they are the same length. Lousy drawing or typo?
Hint: don't evaluate the emf along QR explicitly! Use what post 3 says.

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rude man said:
In the diagram, PQ >> PR yet it says they are the same length. Lousy drawing or typo?
Not very good drawing. The triangle is supposed to be right isosceles.

Naman Singh
kuruman said:
Not very good drawing. The triangle is supposed to be right isosceles.
That is my assumption also (but it's just an assumption). So we assume the given dimensions are gospel, not the drawing.

rude man said:
That is my assumption also (but it's just an assumption). So we assume the given dimensions are gospel, not the drawing.
Yes. It appears that the drawing is not to scale. The problem clearly states that ##PQ=PR=2l##. The only assumption is that angle QPR = 90o. Without it there is no choice that matches the answer.

TSny said:
I guess that the phrase "emf induced in the side PQ" means the magnitude of the integral ∫E.dl, where the integral is taken along the side PQ and E is the induced electric field.

By symmetry, what can you say about the shape of the induced electric field lines?
Can you use ##\oint##E.dl = -dφ/dt to determine the magnitude of E at any point within the magnetic field region?

Thanks for the hints but I'm really not making headway with this. Can you please explain how symmetry plays a part here?

Naman Singh said:
Thanks for the hints but I'm really not making headway with this. Can you please explain how symmetry plays a part here?
Symmetry says that the electric field lines in the region of interest are concentric circles. What does this suggest about ##\int \vec E \cdot d\vec l## along segment PQ? What about along segment RS or any radial line segment?

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## 1. What is electromagnetic induction?

Electromagnetic induction is the process of creating an electric current in a conductor by passing it through a magnetic field or by varying the magnetic field around it.

## 2. How does electromagnetic induction work?

Electromagnetic induction works through the principle of Faraday's law, which states that a changing magnetic field will induce an electric field in a conductor. This electric field can then cause a current to flow through the conductor.

## 3. What are some practical applications of electromagnetic induction?

Some practical applications of electromagnetic induction include generators, transformers, electric motors, induction cooktops, and wireless charging technology.

## 4. What is the relationship between electricity and magnetism in electromagnetic induction?

Electromagnetic induction shows the close relationship between electricity and magnetism. A changing magnetic field can create an electric field, and an electric current can create a magnetic field. This relationship is described by Maxwell's equations.

## 5. How is electromagnetic induction related to the concept of energy transfer?

Electromagnetic induction is related to the concept of energy transfer because it allows for the conversion of mechanical energy into electrical energy. This is seen in generators, where a rotating coil in a magnetic field converts mechanical energy into electricity.

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