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In accordance with Lenz’s law, the negative sign in [link] indicates that the induced emf across an inductor always has a polarity that opposes the change in the current. For example, if the current flowing from A to B in [link] (a) were increasing, the induced emf (represented by the imaginary battery) would have the polarity shown in order to oppose the increase. If the current from A to B were decreasing, then the induced emf would have the opposite polarity, again to oppose the change in current ( [link] (b)). Finally, if the current through the inductor were constant, no emf would be induced in the coil.

Figure a shows an increasing current flowing from point A to point B through a coil. An imaginary battery is shown with its positive terminal towards A and negative one towards B. Figure b shows a decreasing current flowing from point A to point B through a coil. An imaginary battery is shown with its negative terminal towards A and positive one towards B.
The induced emf across an inductor always acts to oppose the change in the current. This can be visualized as an imaginary battery causing current to flow to oppose the change in (a) and reinforce the change in (b).

One common application of inductance is to allow traffic signals to sense when vehicles are waiting at a street intersection. An electrical circuit with an inductor is placed in the road underneath the location where a waiting car will stop. The body of the car increases the inductance and the circuit changes, sending a signal to the traffic lights to change colors. Similarly, metal detectors used for airport security employ the same technique. A coil or inductor in the metal detector frame acts as both a transmitter and a receiver. The pulsed signal from the transmitter coil induces a signal in the receiver. The self-inductance of the circuit is affected by any metal object in the path ( [link] ). Metal detectors can be adjusted for sensitivity and can also sense the presence of metal on a person.

Photograph of people queued up at a metal detector gate at an airport.
The familiar security gate at an airport not only detects metals, but can also indicate their approximate height above the floor. (credit: “Alexbuirds”/Wikimedia Commons)

Large induced voltages are found in camera flashes . Camera flashes use a battery, two inductors that function as a transformer, and a switching system or oscillator to induce large voltages. Recall from Oscillations on oscillations that “oscillation” is defined as the fluctuation of a quantity, or repeated regular fluctuations of a quantity, between two extreme values around an average value. Also recall (from Electromagnetic Induction on electromagnetic induction) that we need a changing magnetic field, brought about by a changing current, to induce a voltage in another coil. The oscillator system does this many times as the battery voltage is boosted to over 1000 volts. (You may hear the high-pitched whine from the transformer as the capacitor is being charged.) A capacitor stores the high voltage for later use in powering the flash.

Self-inductance of a coil

An induced emf of 2.0 V is measured across a coil of 50 closely wound turns while the current through it increases uniformly from 0.0 to 5.0 A in 0.10 s. (a) What is the self-inductance of the coil? (b) With the current at 5.0 A, what is the flux through each turn of the coil?

Strategy

Both parts of this problem give all the information needed to solve for the self-inductance in part (a) or the flux through each turn of the coil in part (b). The equations needed are [link] for part (a) and [link] for part (b).

Solution

  1. Ignoring the negative sign and using magnitudes, we have, from [link] ,
    L = ε d I / d t = 2.0 V 5.0 A / 0.10 s = 4.0 × 10 −2 H .
  2. From [link] , the flux is given in terms of the current by Φ m = L I / N , so
    Φ m = ( 4.0 × 10 −2 H ) ( 5.0 A ) 50 turns = 4.0 × 10 −3 Wb .

Significance

The self-inductance and flux calculated in parts (a) and (b) are typical values for coils found in contemporary devices. If the current is not changing over time, the flux is not changing in time, so no emf is induced.

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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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