Fundamental Electrical and Electronic Principles, Third Edition

Electromagnetism 143When the magnet is withdrawn from the coil, the galvo will again beseen to deflect momentarily. This time, the deflection will be in theopposite direction. Provided that the magnet is removed at the samerate as it was inserted, then the magnitudes of the deflections will bethe same. The polarities of the induced emfs will be opposite to eachother, since the current flow is reversed. Thus far, we have confirmationthat an emf is induced in the coil when a magnetic flux is movingrelative to it. We also have confirmation of part two of the law.In order to deduce the relationship between the value of inducedemf and the rate of change of flux, the magnet needs to be moved atdifferent speeds into and out of the coil. When this is done, and theresulting magnitudes of the galvo deflection noted, it will be found thatthe faster the movement, the greater the induced emf.This simple experiment can be further extended in three ways. If themagnet is replaced by a more powerful one, it will be found that forthe same speed of movement, the corresponding emf will be greater.Similarly, if the coil is replaced with one having more turns, then for agiven magnet and speed of movement, the value of the emf will again befound to be greater. Finally, if the magnet is held stationary within thecoil, and the coil is then moved away, it will be found that anemf is once more induced in the coil. In this last case, it will also befound the emf has the same polarity as obtained when the magnet wasfirst inserted into the stationary coil. This last effect illustrates the pointthat it is the relative movement between the coil and the flux that inducesthe emf.The experimental procedure described above is purely qualitative.However, if it was refined and performed under controlled conditions,then it would yield the following results:The magnitude of the induced emf is directly proportional to the valueof magnetic flux, the rate at which this flux links with the coil, and thenumber of turns on the coil. Expressed as an equation we have:Ne d Φvoltdt(5.1)Notes:1 The symbol for the induced emf is shown as a lower-case letter e.This is because it is only present for the short interval of timeduring which there is relative movement taking place, and so hasonly a momentary value.2 The term d Φ /d t is simply a mathematical means of stating ‘ therate of change of flux with time ’ . The combination NΦ/ d t is oftenreferred to as the ‘ rate of change of flux linkages ’ .3 The minus sign is a reminder that Lenz ’ s law applies. This law isdescribed in the next section.