# Electromagnetic Theory

Article by Ivor Catt in Wireless World, March 1983

#### Waves in space

In an open circuit, only an electric field is detectable.

Is this because there is no magnetic field?

Prior to Maxwell, a great deal of theory had been developed around electric and magnetic fields. This theory included Kirchhoff’s Laws, the Biot-Savart Law and Ampere’s Rule. Electrical circuits were generally steady state, or at worst slowly varying, and the problem of whether electrical and magnetic effects traversed distance instantaneously or took time to propagate did not arise.

Because fields were steady or slowly varying, experiments were generally limited to the study of closed  circuits of conductors (and resistors). However, capacitors (electrolytics) were also used, and these created an anomaly in a theoretical structure which included Ampere’s circuital law (Integral Hdl = I) and Kirchhoff’s second law (SI= 0). When the switches were closed, electric current flowed in the loop and (following Ampere’s Rule,) magnetic flux appeared in the space around the wires.

Ampere’s Rule says that if we describe a closed loop, the line integral of the magnetic field strength along the edge of the loop is related to the electric current through any surface bounded by the loop.

The capacitor created an anomaly, because a closed loop could be described where I had more than one value, depending on whether the surface (S1) cut the conductor or (S2) passed between the plates of the capacitor. Consequently the absurd situation arose that (Integral Hdl) had to have two values at the same time.

Maxwell ‘cut the Gordian knot’ by asserting that the rate of change of electric field between the capacitor plates behaved just like a real current i. So Ampere’s Rule became

Integral Hdl = I + (Integral around the loop) (dD/dt) ds

It is important to remember that the premise which preceded the problem of the capacitor was that electric currents and fields were steady or slowly varying. It was accepted that, at the moment the switches closed, the current I appeared at all points in the circuit. The time for the effect of the switch closure to travel across the distance from switches to capacitor was zero.

The current-like field dD/dt between the capacitor plates led Maxwell to conjecture that there could be electromagnetic ‘waves in space’. It was already known that a changing magnetic field produced electric current (Faraday’s Law v = - dj/dt) and that electric current produced a magnetic field (  Biot-Savart Law dH = I dl sinq / 4pr2  ) The changing electric field dD/dt seemed to be an electric current in space. With both changing magnetic fields and changing electric currents in space, we seemed to have the possibility of electromagnetic signals using a crabwise progression of cause and effect; electric current – magnetic field – electric current.

The error in this whole business occurred right at the start. Let us assume that the conductors linking battery to capacitor are one light year long. When the switches are closed, it is obvious that current will not immediately flow in the capacitor. A wave front must travel from switches to capacitor, and behind that front will be electric and magnetic field – we have a transmission line. Also, should the distance between the two conductors or their shape change, some of the wave front will continue to the right and some will reflect to the left, carrying back the message about the change.

The front end of a capacitor is merely one such change in the cross section of the transmission line. The far (open circuit) end of the capacitor is another such change.

The problem Maxwell should have been concerned about was how the electromagnetic field developed between the wires when the switches were closed, not what happened in a capacitor. The transmission line problem (AB) precedes the capacitor problem (CD), and the capacitor problem would be solved automatically with the solution of the transmission line problem.

Before the switches are closed, we can measure a voltage and an electric field but find no trace of a magnetic field. When the switches are closed, an electric current starts off down the wires and a magnetic field begins to appear between the wires. The conclusion that the voltage (or pressure) causes the electric current which in turn causes the magnetic field is compelling, and it is not surprising that this mistaken view has lasted for a century. It is then a short step to say that the changing magnetic field in its turn (by Faraday’s Law) generates an electric field and thence a (displacement) current, and the sequence can start again.

But was there really no magnetic field before the switches were closed?

Let us consider a steady charged capacitor. Does it have no magnetic field, only an electric field? In order to understand the situation in the battery and wires up to the switches before they are closed, it is useful to study the reed-relay pulse generator.

(Return from reading about the reed relay pulse generator at http://www.ivorcatt.com/2_4.htm when you reach; “…. Bounced off the open circuit at A”)

Even before the switches were closed, every segment of electric field had coexisting with it a segment of magnetic field at right angles, and both were travelling together at the speed of light.

What is true of a ‘steady’ charged capacitor or coax. Cable is also true of a pair of wires connected to the battery (Figure 2). Before closure of the switches, electromagnetic (not electric) energy was oscillating to and fro between battery and switches. Since the same amount travelled in both directions, the magnetic fields being equal and opposite cancelled, and only an electric field could be detected. ‘Waves in space’ existed between these two wires before the switches were closed and before the capacitor came into the picture.

Comments on article by Ivor Catt in Wireless World, March 1983 at www.ivorcatt.com/3803.htm