In a given electromagnetic plane wave the maximumelectric field strength is 400

V/m.
What is the maximum magnetic field strength? How does the energy stored
in the magnetic field compare with the energy stored in the electric field at
any given time?
how do you calculate the average intensity of the wave.
and how do you calculate the average energy density of the wave.

You have to have a nice summary in your electromagnetic energy chapter that summarizes this, look in the section of your text that discusses Poynting flux, or Poynting vector.

Isn't E^2=B^2 ? That is, half the energy is in the electric field and half in the magnetic field?

To find the maximum magnetic field strength (B), you can use the relation between the electric field (E) and magnetic field (B) in an electromagnetic wave:

B = E / c

where c is the speed of light in vacuum (~3 x 10^8 m/s).

In this case, the maximum electric field strength (E) is given as 400 V/m. Plugging this value into the equation, we can calculate the maximum magnetic field strength:

B = 400 V/m / (3 x 10^8 m/s) = 1.33 x 10^-6 T (Tesla)

To compare the energy stored in the magnetic field (Em) with the energy stored in the electric field (Ee) at any given time, we can use the following equations:

Em = (1/2) * μ0 * B^2
Ee = (1/2) * ε0 * E^2

where μ0 is the permeability of free space (4π x 10^-7 T·m/A), ε0 is the permittivity of free space (8.85 x 10^-12 C^2/N·m^2), B is the magnetic field strength, and E is the electric field strength.

Since the energy is directly proportional to the square of the field strength, the ratio of the energy stored in the magnetic field to the energy stored in the electric field is:

Em / Ee = (B^2 / E^2) * (μ0 / ε0)

Substituting the values we have:

Em / Ee = [(1.33 x 10^-6 T)^2 / (400 V/m)^2] * [(4π x 10^-7 T·m/A) / (8.85 x 10^-12 C^2/N·m^2)]

By plugging these values into the calculator, you can find the ratio.

To calculate the average intensity (I) of the wave, you can use the formula:

I = (1/2) * c * ε0 * E^2

where E is the electric field strength. In this case, the given E is 400 V/m, so we can substitute it to find the average intensity.

I = (1/2) * (3 x 10^8 m/s) * (8.85 x 10^-12 C^2/N·m^2) * (400 V/m)^2

Calculating this expression will give you the average intensity of the wave.

The average energy density (u) of the wave is given by:

u = (1/2) * (ε0 * E^2 + B^2 / μ0)

Using the values previously obtained for E and B, you can substitute them into the formula to calculate the average energy density.