One turn of the coil

Figure 13.21 shows how the emf induced in the coil changes as it turns anticlockwise through one full turn in the magnetic field.

Figure to be added

Figure 13.21 (top) — the coil at five positions (a) to (e), 90° apart, drawn edge-on in a field running left to right, with the motion of sides AB and CD marked.

θ (°)	90	270
e	1	-1

Figure 13.21 (bottom) — the induced emf e against the angle turned: zero at 0°, +V_m at 90°, zero at 180°, −V_m at 270° and zero again at 360°.

Position (a), 0°

AB and CD move parallel to the field, so no field lines are cut, no emf is induced, and the galvanometer reads zero.

(a) to (b), 0° to 90°

The rate of cutting field lines rises, and so does the deflection. At (b) AB moves up and CD down, cutting the lines at right angles: the current ABCD is greatest and the galvanometer swings left.

(b) to (c), 90° to 180°

The emf falls back to zero at (c), as at (a).

Now AB moves down and CD up: the current flows DCBA, and the galvanometer swings right, greatest at (d).

So as the coil keeps turning, the current in the outside circuit keeps changing direction: the galvanometer swings left at (b), to zero at (a), (c) and (e), and right at (d), over and over. In one full turn, the current reverses every half turn. How this alternating current or induced emf changes with time can be drawn as a graph shaped like a sine wave. When the plane of the coil is parallel to the field the emf is at its (+) or (−) maximum; when the plane of the coil is at right angles to the field, the emf is zero.

Parallel to the field means greatest

It feels backwards, but the emf is greatest when the flat face of the coil lies along the field, because then AB and CD are moving straight across the field lines.

One turn, one sine wave

The emf is zero with the coil upright, greatest with it lying along the field, and reverses every half turn — an alternating current.