James Clerk Maxwell
James Clerk Maxwell

Start this free course now. Just create an account and sign in. Enrol and complete the course for a free statement of participation or digital badge if available.

Free course

James Clerk Maxwell

5.1.2 Getting agreement with Gauss's law

Substituting the assumed form of the electric field (Equation 7.20) into the empty-space version of Gauss's law (Equation 7.16) gives

The first two partial derivatives are equal to zero because f does not depend on x or y. So we obtain

We are interested in disturbances that propagate in the z-direction, so can ignore the possibility that ∂f/∂z = 0 everywhere. It follows that uz = 0. This means that u is a unit vector perpendicular to the z-direction. With no loss in generality, we can choose u to be equal to ex. It is then appropriate to replace f by Ex, and write Equation 7.20 in the form

A wave of this type, in which the variable of interest oscillates perpendicular to the direction of propagation, is said to be transverse.

SMT359_2

Take your learning further371

Making the decision to study can be a big step, which is why you'll want a trusted University. The Open University has 50 years’ experience delivering flexible learning and 170,000 students are studying with us right now. Take a look at all Open University courses372.

If you are new to university level study, we offer two introductory routes to our qualifications. Find out Where to take your learning next?373 You could either choose to start with an Access courses374or an open box module, which allows you to count your previous learning towards an Open University qualification.

Not ready for University study then browse over 1000 free courses on OpenLearn375 and sign up to our newsletter376 to hear about new free courses as they are released.

Every year, thousands of students decide to study with The Open University. With over 120 qualifications, we’ve got the right course for you.

Request an Open University prospectus371