# Induced EMF in a moving Loop Conductor

• Kharrid
In summary, the conversation discusses the concept of induced current in a circular loop. One explanation suggests that no induced electric field is created when the loop is moving to the right, as the flux remains constant. However, the online link provided discusses induced emf in a rod moving through a magnetic field. The conversation concludes that in a rectangular loop with mutually orthogonal vectors, the induced emf is zero.
Kharrid
Homework Statement
A circular wire loop is placed in a uniform magnetic field. Find if there is an induced current. The normal of the loop points along the positive x-axis and the magnetic field also points along the positive x-axis.

1. loop moves to the right

2. loop moves to the left
Relevant Equations
F = qv x B
Flux = BAN
emf = ∫ E ds = -d Φ / dt
I am having trouble figuring out if the circular loop has an induced current.

One explanation is ∫ E ds = -d Φ / dt. Since flux = B ⋅ A, a change in the magnetic field would require a change in the magnetic field, a change in the area, or change in direction of either vector. Since none of these happen, the flux while the loop is moving to the right is constant and no electric field is induced that would create an induced current.

After looking online, it seems that there is always an induced emf when a loop is moved through a uniform magnetic field but I'm not sure why. If I try to follow the logic from my book, I'm supposed to find the induced electric field that causes the charges to move. Well, the induced electric field is the negative rate of change in flux. Since the magnetic field is uniform, the area vector is the same, and there is no change in direction between the vectors while the loop is moving, there is no change in flux. Hence, no induced emf.

Am I missing something?

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I agree with your analysis using Faraday's law. The flux linked is constant.

The link you attach is referring to a rod moving through a magnetic field. The emf induced in a rod if the rod, magnetic field and velocity vector are all mutually orthogonal is ##\mathcal{E} = Blv##.

You might consider your loop to be a rectangular frame made up of 4 individual wires/rods, with one pair of sides parallel to the velocity vector and the other two orthogonal to the velocity vector. Suppose the magnetic field is normal to the plane of the loop. What is the EMF induced in each loop (pay attention to their directions...)? What is the total EMF around the loop?

The work is in the photo. Essentially, I think the emf of the two horizontal sides is 0 and the emf of the two vertical sides is vBL. Since the vertical sides have the same direction and magnitude, they cancel and the total emf is zero around the loop. Is this correct?

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That's essentially correct, yes. Hopefully that satisfies you that everything is still consistent!

The way I like to think of it is in terms of the vector triple product, ##\mathcal{E} = (\vec{v} \times \vec{B}) \cdot \vec{l} = vBl\sin{\theta}\cos{\phi}##. If all 3 vectors are mutually orthogonal this reduces to ##\mathcal{E} = Blv##. If at least two of ##\vec{v}##, ##\vec{l}##, and ##\vec{B}## are parallel, the whole expression becomes zero.

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Kharrid

## 1. What is induced EMF in a moving loop conductor?

Induced EMF, or electromotive force, in a moving loop conductor is the voltage generated in a loop of wire when it is moved through a magnetic field. This movement creates a change in the magnetic flux through the loop, resulting in the generation of an electric current.

## 2. How is induced EMF calculated?

Induced EMF can be calculated using Faraday's Law, which states that the magnitude of the induced EMF is equal to the rate of change of magnetic flux through the loop. This can be represented by the equation E = -N(dΦ/dt), where E is the induced EMF, N is the number of turns in the loop, and dΦ/dt is the change in magnetic flux over time.

## 3. What factors affect the magnitude of induced EMF?

The magnitude of induced EMF is affected by several factors, including the strength of the magnetic field, the speed of the loop through the field, the angle between the loop and the field, and the number of turns in the loop. Additionally, the material of the loop conductor and any external resistances can also impact the induced EMF.

## 4. What is Lenz's Law and how does it relate to induced EMF?

Lenz's Law states that the direction of the induced current in a loop is always such that it opposes the change in magnetic flux that caused it. This means that the induced current creates a magnetic field that opposes the original magnetic field, resulting in a decrease in the induced EMF. This law is important in understanding the behavior of induced EMF in a moving loop conductor.

## 5. What are some practical applications of induced EMF?

Induced EMF has many practical applications, including power generation in electric generators, induction heating in cooktops, and magnetic braking in trains. It is also used in various sensors, such as inductive proximity sensors and magnetic flow meters. Additionally, the concept of induced EMF is essential in understanding the principles of electromagnetic induction, which is the basis for many modern technologies.

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