The factors determining the induced EMF in a wire

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In summary: But you do have closed circuits in your examples. Regardless, you can compute the emf in the wire by considering the magnetic flux through the area swept by the wire per time unit.
The induced emf in a straight wire is determined by the equation (emf=Blv sinθ) where θ is the angle between the direction of the motion and the lines of the magnetic field, and frequently, I see diagrams like these explaining the phenomenon:

In those pictures the wire is perpendicular to the lines of the field, so it starts its motion of that state, and I was wondering what if the wire was like this:

In that diagram the angle between the wire and the field is not 90 it is θ1 and the angle between the direction of the motion and the magnetic field lines is θ2.
So, in the equation (emf=Blv sinθ) which angle will be involved here? θ1 or θ2? Or θ1=θ2? And then there will be no difference.
Note: in the last diagram the wire moves from position 1 to position 2.

Last edited:
The basic tule id that the induced emf is dependent on the change of magnetic flux through the circuit. Then you may compute it and get some special case results in given setups.

Orodruin said:
The basic tule id that the induced emf is dependent on the change of magnetic flux through the circuit. Then you may compute it and get some special case results in given setups.
Actually I don't have given setups, this question came to my mind while studying the induced emf in a straight wire, and all the figures show that the wire starts its motion from the position where it is perpendicular to the field lines.
I wonder whether the equation still the same if the wire starts its motion from the position where there is an angle <90 between it and the magnetic field lines.

Actually I don't have given setups, this question came to my mind while studying the induced emf in a straight wire, and all the figures show that the wire starts its motion from the position where it is perpendicular to the field lines.
I wonder whether the equation still the same if the wire starts its motion from the position where there is an angle <90 between it and the magnetic field lines.

But you do have closed circuits in your examples. Regardless, you can compute the emf in the wire by considering the magnetic flux through the area swept by the wire per time unit.

The induced emf in a straight wire is determined by the equation (emf=Blv sinθ) where θ is the angle between the direction of the motion and the lines of the magnetic field, and frequently, I see diagrams like these explaining the phenomenon:

In those pictures the wire is perpendicular to the lines of the field, so it starts its motion of that state, and I was wondering what if the wire was like this:

In that diagram the angle between the wire and the field is not 90 it is θ1 and the angle between the direction of the motion and the magnetic field lines is θ2.
So, in the equation (emf=Blv sinθ) which angle will be involved here? θ1 or θ2? Or θ1=θ2? And then there will be no difference.
Note: in the last diagram the wire moves from position 1 to position 2.
In motional emf equation, θ is the angle between the velocity vector and magnetic field vector.

cnh1995 said:
In motional emf equation, θ is the angle between the velocity vector and magnetic field vector.
So, we would ignore the angle between the wire and the magnetic field lines and only consider the angle between the direction of motion and the magnetic field lines?

cnh1995 said:
In motional emf equation, θ is the angle between the velocity vector and magnetic field vector.
This is not precisely true. It is true only when the wire is orthogonal to both velocity and field. The actual induced emf would be proportional to the triple product ##\vec B\cdot (d\vec \ell\times \vec v)##. The cross product would be the area element swept per unit time and taking its scalar product with ##\vec B## gives the flux.

1. What is induced EMF and how is it different from EMF?

Induced EMF (electromotive force) is the voltage generated in a wire when it is subjected to a changing magnetic field. It is different from EMF, which is the potential difference between two points in a circuit. Induced EMF is a result of the changing magnetic field, while EMF is a constant value in a circuit.

2. What are the factors that determine the induced EMF in a wire?

The factors that determine induced EMF in a wire are the strength of the magnetic field, the velocity of the wire with respect to the magnetic field, and the angle between the wire and the magnetic field lines. These factors can affect the magnitude and direction of the induced EMF.

3. How does the strength of the magnetic field affect the induced EMF?

The strength of the magnetic field is directly proportional to the induced EMF. This means that a stronger magnetic field will result in a larger induced EMF, while a weaker magnetic field will result in a smaller induced EMF.

4. How does the velocity of the wire affect the induced EMF?

The velocity of the wire with respect to the magnetic field is also directly proportional to the induced EMF. This means that a higher velocity will result in a larger induced EMF, while a lower velocity will result in a smaller induced EMF.

5. Why is the angle between the wire and the magnetic field important in determining induced EMF?

The angle between the wire and the magnetic field lines affects the component of the magnetic field that is perpendicular to the wire. This component is what causes the induced EMF, so the angle can greatly impact the magnitude and direction of the induced EMF.

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