# Solving Electromagnetics Problems: Finding P from E

• robert25pl
In summary, the conversation is discussing how to solve electromagnetics problems and specifically how to find the values of parameters for which the Poynting vector is time independent. The solution involves finding the electric and magnetic fields, setting the time dependence of the Poynting vector to zero, and considering the phase. It is mentioned that the fact that the problem is in vacuum should not affect the solution too much.
robert25pl
I have to solve many electromagnetics problems but some of them are not clear to me. For example,

For what values of the parameters is the Poynting vector time independent?
If given electric field of a uniform plane wave propagating in the positive z direction in vacuum.

E is given. So I have to find H and then just P = E x H ?

Well,u'll need to cancel the time dependence of the Poynting vector.Compute it's phase and set the time part to 0.

Daniel.

Ok this is my E

$$E = E_{1} cos(\omega t - \beta z) \vec{i} + E_{2} sin(\omega t - \beta z) \vec{j}$$

Okay.Compute the B and then the P.And set the time dependence of P to zero.

Daniel.

Will my answer change because E in vacuum?

It shouldn't matter too much,you're interested in the phase.Anyway,do those derivatives,that integration and then see what else needs to be done.

Daniel.

## 1. What is the relationship between P and E in electromagnetics?

P and E are two components of the electromagnetic field. P represents the electric dipole moment, which is a measure of the separation of positive and negative charges in a system. E represents the electric field, which is the force exerted on a charged particle by an electric field. In simple terms, P is the cause of E, and E is the effect of P.

## 2. How do I solve for P from given values of E in an electromagnetics problem?

To solve for P from E, you can use the equation P = ε0E, where ε0 is the permittivity of free space. This equation relates the electric dipole moment to the electric field strength. Simply substitute the given value of E in the equation to calculate P.

## 3. Can P and E have opposite directions?

Yes, P and E can have opposite directions. In this case, the electric dipole moment and the electric field are pointing in opposite directions, but they are still related to each other. This can occur in situations where there is an unequal distribution of positive and negative charges.

## 4. Are there any other methods for solving for P besides using the equation P = ε0E?

Yes, there are other methods for solving for P in electromagnetics problems. One method is to use the equation P = Qd, where Q is the total charge of the system and d is the distance between the positive and negative charges. Another method is to use vector calculus and the equation P = ∫rdV, where r is the position vector and dV is the volume element.

## 5. Can P be zero even if E is not zero?

Yes, it is possible for P to be zero even if E is not zero. This can occur in situations where the positive and negative charges are perfectly balanced and cancel each other out, resulting in a net electric dipole moment of zero. However, this is not always the case, and it is important to consider the values and directions of both P and E in an electromagnetics problem.

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