# Induced EMF in an Open Loop

• B
• person123

#### person123

Let's say you have an open loop (like a section of a circle) in a changing magnetic field. I think there would be an induced EMF, but no current. What I can't figure out, though, is how to calculate the induced EMF. Using Faraday's law doesn't seem to help, as there's no enclosed area.

Suppose there is EMF (voltage difference) between the ends. What do you think will happen? Would current flow through the wire?

scottdave said:
Suppose there is EMF (voltage difference) between the ends. What do you think will happen? Would current flow through the wire?
No, as there's no path for current to flow.

You would need to find the electric field (##\vec{E}##) due to changing magnetic field (by solving Maxwell's Equations), and then compute the voltage across the open loop ##C## by integrating the electric field along it ##V=-\int_C \vec{E}.\vec{\hat{l}} dl##

There is a capacitance due to the ends of the wire. Current will flow, due to Xc = 1/(omega*C)

## 1. What is induced EMF in an open loop?

Induced EMF in an open loop refers to the electromotive force (EMF) that is produced in a conducting loop when it is exposed to a changing magnetic field. This phenomenon is also known as Faraday's law of induction.

## 2. How is induced EMF in an open loop generated?

Induced EMF in an open loop is generated when there is a relative motion between the loop and a magnetic field, causing the magnetic flux through the loop to change. This change in flux induces an electric field within the loop, resulting in the production of an EMF.

## 3. What factors affect the magnitude of induced EMF in an open loop?

The magnitude of induced EMF in an open loop is affected by the rate of change of magnetic flux, the number of turns in the loop, and the strength of the magnetic field. A faster rate of change, more turns, and a stronger magnetic field will result in a larger induced EMF.

## 4. What is the direction of induced EMF in an open loop?

The direction of induced EMF in an open loop is determined by the right-hand rule. If the magnetic field is increasing, the induced current will flow in a direction that creates a magnetic field that opposes the change in the original magnetic field. If the magnetic field is decreasing, the induced current will flow in a direction that creates a magnetic field that reinforces the original magnetic field.

## 5. How does induced EMF in an open loop relate to Lenz's law?

Induced EMF in an open loop is a result of Lenz's law, which states that the induced current flows in a direction that opposes the change in the magnetic field that produced it. This law helps to explain the observed direction of induced EMF and the effects of induced currents in circuits.