A plane wave in vacuum has electric field E = (75 , V ,m^ -1 ) ( k r - t)

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Optics & Photonics · Polarisation and anisotropic media

Electricity, Magnetism and Electromagnetism, Ch Plane electromagnetic waves: polarisation, energy flux and radiation pressure

Problem

A plane wave in vacuum has electric field

\mathbf{E} = (75\,\mathrm{V\,m^{-1}})\cos(\mathbf{k}\cdot\mathbf{r} - \omega t)\,\hat{\mathbf{y}}, \qquad \mathbf{k} = (3.0\,\hat{\mathbf{x}} + 4.0\,\hat{\mathbf{z}})\,\mathrm{rad\,m^{-1}},

with

\omega = ck

and

c = 3.00\times10^8\,\mathrm{m\,s^{-1}}

. ((a)) Find the wavelength and the frequency. ((b)) Find the amplitudes of the

x

and

z

components of

\mathbf{B}

, with their signs (the

y

component is zero). ((c)) A polarising filter is placed across the beam with its plane perpendicular to

\mathbf{k}

and its transmission axis lying in that plane at

40^\circ

\hat{\mathbf{y}}

. What fraction of the incident intensity passes?