# Find expression for electric field given B(t)

• mkematt96
In summary, the conversation discusses a potential mistake in applying Stoke's formulas, particularly in the relevant equation (2) where the variable B should be replaced with -dB/dt. The direction of the line integrals in the figure is also mentioned, with the suggestion that they should go counterclockwise with +z out of the paper.
mkematt96

## Homework Statement

See picture above

## Homework Equations

Int (E dot dl) = Int (B dot dA)

## The Attempt at a Solution

Where did I go wrong? Is there a sign error possibly or am I off conceptually? [/B]

The only thing I see that is incorrect is in your relevant equations (2), it should say ## -dB/dt ## instead of ## B ##. Their ## dl ## in the figure is in the opposite direction of what it should be, but I don't think that is your mistake. The line integrals in these Stoke's formulas always go counterclockwise with +z out of the paper. Perhaps the instructor wanted you to spot that anomaly, etc...

## 1. What is the equation for electric field in terms of a changing magnetic field?

The equation for electric field in terms of a changing magnetic field is given by E = -∆B/∆t, where E is the electric field, B is the magnetic field, and ∆t is the change in time.

## 2. How do you find the direction of the electric field from a changing magnetic field?

The direction of the electric field from a changing magnetic field can be determined using the right-hand rule. If the fingers of your right hand point in the direction of the changing magnetic field, then your thumb will point in the direction of the electric field.

## 3. Can the electric field exist without a changing magnetic field?

No, according to Faraday's law of induction, a changing magnetic field will always produce an electric field. Therefore, an electric field cannot exist without a changing magnetic field.

## 4. What is the relationship between the magnitude of the electric field and the rate of change of the magnetic field?

The magnitude of the electric field is directly proportional to the rate of change of the magnetic field. This means that a larger change in the magnetic field will result in a stronger electric field.

## 5. How is the equation for electric field given a changing magnetic field related to electromagnetic waves?

The equation for electric field given a changing magnetic field is a fundamental part of Maxwell's equations, which describe the behavior of electromagnetic waves. Electromagnetic waves are created by oscillating electric and magnetic fields, and the equation for electric field is essential in understanding their behavior.

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