## The propagating magnetic field

The moment the electric current is switched on, the resulting magnetic field spreads out in all directions like a tidal wave. In Figure 10.20 a segment of the leading edge of the magnetic field, moving from left to right, has reached a certain point.

To the left there is now a magnetic field in the direction perpendicular to the page; to the right there is none. The 'tidal wave' has not yet reached beyond that point.

Let us place a Faraday loop at some point on the advancing edge of the 'magnetic tidal wave'. (Lower half of Figure 10.20) We can make the loop as small as we like so that we do not have to worry whether B is constant across the loop.

Faraday's law states that as the magnetic flux through the loop changes it will induce an electric field E such that

The electric field E is zero along the side bc of the loop and is perpendicular to the sides ab and cd, and therefore contributes to the integral only along ad.

Direction of the 1 L original current i v

The magnetic field B and the electric field E are perpendicular to each other and to the v

direction of propagation.

Figure 10.21 Electric field induced at right angles to the magnetic field.

We have deduced that the incoming magnetic field B generates an electric field E which is perpendicular to the magnetic field and in the direction opposite to that of the original current. In addition, by solving the simultaneous equations relating to Figure 10.20 we have obtained an expression for v. The two fields will propagate together at a certain fixed speed which is equal to the ratio of the magnitudes of the two fields:

The next step is described in Figure 10.22. A new player has now appeared and is contributing to the action. It is an v

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