# Getting E-Field from magnetic field intensity, H

• electrifice
In summary, to find E-field from given magnetic field intensity H, we can use the relationship \muH = B and take the partial derivative of that with respect to time. Using Stokes's theorem can help "uncurl" E. It is recommended to post questions about Calculus 3 and advanced physics in the appropriate forums.
electrifice

## Homework Statement

Given the magnetic field intensity, H, find E.
H=$$\hat{y}$$6cos(2z)sin((2x10^7)t - 0.1x)

## Homework Equations

$$\nabla$$ $$\times$$ E = $$\frac{- \partial B}{\partial t}$$

## The Attempt at a Solution

Since we have H, we can use the relationship that $$\mu$$H = B and then take the partial derivative of that with respect to time. That would give us this quantity...

$$\frac{- \partial B}{\partial t}$$

Now, how do I get to E-field from that? How do you "uncurl" that?

You could use Stokes's theorem to "uncurl" E. Do you see where it's headed?

Also, just to help you out in the future, anything with Calc 3 doesn't really belong in intro physics, and you may be helped quicker in advanced physics for questions like this.

To find the electric field, we can use Maxwell's equations, specifically the Faraday's law of induction which states that the curl of the electric field is equal to the negative of the time derivative of the magnetic field. In mathematical notation, this can be written as:

\nabla \times E = -\frac{\partial B}{\partial t}

Using this equation, we can solve for the electric field by taking the curl of both sides and rearranging to isolate for E. This would give us the following expression:

E = -\frac{1}{\mu}\nabla \times H

Where \mu is the magnetic permeability of the medium. This means that the electric field can be obtained by taking the curl of the given magnetic field intensity and dividing by the magnetic permeability. Keep in mind that the electric field will also have a time-dependent component, as shown in the given expression.

## 1. How do you calculate the E-field from the magnetic field intensity, H?

To calculate the E-field from the magnetic field intensity, H, you can use the equation E = cH, where c is the speed of light in the medium. This equation is derived from Maxwell's equations and is known as the wave impedance. It represents the relationship between the electric and magnetic fields in an electromagnetic wave.

## 2. What is the relationship between the E-field and the magnetic field intensity, H?

The E-field and magnetic field intensity, H, are both components of an electromagnetic wave. They are perpendicular to each other and together they create an electromagnetic field. The strength of the E-field is directly proportional to the strength of the H-field, as shown in the equation E = cH.

## 3. How does the E-field vary with distance from the source?

The E-field decreases with distance from the source according to the inverse square law. This means that the E-field strength is inversely proportional to the square of the distance from the source. As you move further away from the source of the magnetic field, the E-field strength decreases.

## 4. Can the E-field and magnetic field intensity, H, be measured separately?

Yes, the E-field and magnetic field intensity, H, can be measured separately. This is because they are both components of an electromagnetic wave and can be measured using different instruments. The E-field can be measured using an electric field meter, while the H-field can be measured using a magnetic field meter.

## 5. How does the E-field from a magnetic field differ from the E-field from an electric field?

The E-field from a magnetic field is created by a changing magnetic field, while the E-field from an electric field is created by a static electric charge. The E-field from a magnetic field is also perpendicular to the direction of the magnetic field, while the E-field from an electric field is parallel to the direction of the electric field. Additionally, the E-field from a magnetic field is dependent on the speed of light in the medium, while the E-field from an electric field is not.

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