Write the Poynting vector and state what its direction represents.

For a sinusoidal plane wave with electric-field amplitude \(E_0\), write the average intensity.

A beam of intensity \(850\,\mathrm{W\,m^{-2}}\) falls on area \(0.40\,\mathrm{m^2}\). Find the incident power.

Find the radiation pressure on a perfectly absorbing surface for \(I=1200\,\mathrm{W\,m^{-2}}\).

For the same intensity \(I=1200\,\mathrm{W\,m^{-2}}\), find the pressure on a perfectly reflecting surface at normal incidence.

A sinusoidal wave has \(E_0=200\,\mathrm{V\,m^{-1}}\). Find its average intensity.

A sinusoidal wave has average intensity \(10.6\,\mathrm{W\,m^{-2}}\). Find \(E_0\).

A wave has \(\vec E\) along \(+x\) and \(\vec B\) along \(-y\). What direction is \(\vec S\)?

Show that the electric and magnetic energy densities are equal in a vacuum plane wave.

Derive the instantaneous magnitude \(S=c\epsilon_0E^2\) for a vacuum plane wave.

A beam with intensity \(600\,\mathrm{W\,m^{-2}}\) strikes an absorbing square sail of side \(2.0\,\mathrm{m}\). Find the force.

The same sail is perfectly reflecting. Find the force and explain the factor change.

A laser emits \(5.0\,\mathrm{mW}\) into a circular beam of radius \(1.0\,\mathrm{mm}\). Find the average intensity and electric-field amplitude.

A beam is incident on a perfect mirror at angle \(\theta\) to the surface normal. Explain why the normal radiation pressure is proportional to \(\cos^2\theta\).

A perfect mirror receives sunlight of intensity \(900\,\mathrm{W\,m^{-2}}\) at \(60^\circ\) to the normal. Find the normal radiation pressure.

A spacecraft sail of mass \(20\,\mathrm{kg}\) and area \(100\,\mathrm{m^2}\) perfectly reflects sunlight of intensity \(1360\,\mathrm{W\,m^{-2}}\) at normal incidence. Estimate its acceleration ignoring gravity.

A pulse of light with energy \(2.0\,\mathrm{J}\) is fully absorbed by a block. Find the momentum delivered. Then state the result if it is perfectly reflected backward.

Show that the momentum density of a plane electromagnetic wave can be written \(g=u/c\).

A detector measures average intensity \(I\), but the electric field is not sinusoidal; it is a square wave alternating between \(+E_0\) and \(-E_0\). Compare its intensity with a sinusoidal wave of the same \(E_0\).

Derive a symbolic expression for the electric-field amplitude needed for light pressure to balance weight \(mg\) on a perfectly reflecting horizontal sail of area \(A\).