# 9.8 Induced voltage and magnetic flux

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• Describe methods to produce an electromotive force (emf) with a magnetic field or magnet and a loop of wire.

The apparatus used by Faraday to demonstrate that magnetic fields can create currents is illustrated in [link] . When the switch is closed, a magnetic field is produced in the coil on the top part of the iron ring and transmitted to the coil on the bottom part of the ring. The galvanometer is used to detect any current induced in the coil on the bottom. It was found that each time the switch is closed, the galvanometer detects a current in one direction in the coil on the bottom. Each time the switch is opened, the galvanometer detects a current in the opposite direction. Interestingly, if the switch remains closed or open for any length of time, there is no current through the galvanometer. Closing and opening the switch induces the current. It is the change in magnetic field that creates the current. More basic than the current that flows is the voltage that causes it. The current is a result of an voltage induced by a changing magnetic field , whether or not there is a path for current to flow.

An experiment easily performed and often done in physics labs is illustrated in [link] . A voltage is induced in the coil when a bar magnet is pushed in and out of it. Voltages of opposite signs are produced by motion in opposite directions, and the voltages are also reversed by reversing poles. The same results are produced if the coil is moved rather than the magnet—it is the relative motion that is important. The faster the motion, the greater the voltage, and there is no voltage when the magnet is stationary relative to the coil.

The method of inducing a voltage used in most electric generators is shown in [link] . A coil is rotated in a magnetic field, producing an alternating voltage (and current), which depends on rotation rate and other factors that will be explored in later sections. Note that the generator is remarkably similar in construction to a motor.

So we see that changing the magnitude or direction of a magnetic field produces a voltage. Experiments revealed that there is a crucial quantity called the magnetic flux    , $\Phi$ , given by

$\mathit{\Phi }={B}_{\perp }A,$

where $B$ is the magnetic field strength over an area $A$ , at an angle $\theta$ with the perpendicular to the area as shown in [link] . Any change in magnetic flux $\Phi$ induces a voltage. This process is defined to be electromagnetic induction    . Units of magnetic flux $\Phi$ are $\text{T}\cdot {\text{m}}^{2}$ .

All induction, including the examples given so far, arises from some change in magnetic flux $\Phi$ . For example, Faraday changed $B$ and hence $\Phi$ when opening and closing the switch in his apparatus (shown in [link] ). This is also true for the bar magnet and coil shown in [link] . When rotating the coil of a generator, the angle $\theta$ and, hence, $\Phi$ is changed. Just how great a voltage and what direction it takes depend on the change in $\Phi$ and how rapidly the change is made, as examined in the next section.

## Section summary

• The crucial quantity in induction is magnetic flux $\mathit{\Phi }$ , defined to be $\mathit{\Phi }={B}_{\perp }A$ , where ${B}_{\perp }$ is the magnetic field strength perpendicular to the area $A$ .
• Units of magnetic flux $\Phi$ are $\text{T}\cdot {\text{m}}^{2}$ .
• Any change in magnetic flux $\Phi$ induces a voltage—the process is defined to be electromagnetic induction.

## Conceptual questions

How do the multiple-loop coils and iron ring in the version of Faraday’s apparatus shown in [link] enhance the observation of induced voltage?

When a magnet is thrust into a coil as in [link] (a), what is the direction of the force exerted by the coil on the magnet? Draw a diagram showing the direction of the current induced in the coil and the magnetic field it produces, to justify your response. How does the magnitude of the force depend on the resistance of the galvanometer?

Explain how magnetic flux can be zero when the magnetic field is not zero.

Is a voltage induced in the coil in [link] when it is stretched? If so, state why and give the direction of the induced current.