23.1 Induced emf and magnetic flux  (Page 2/4)

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

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 an emf. This process is defined to be electromagnetic induction    . Units of magnetic flux $\Phi$ are $\text{T}\cdot {\text{m}}^2$ . As seen in [link] , $B\text{cos}\theta =B_{}$ _⊥ , which is the component of $B$ perpendicular to the area $A$ . Thus magnetic flux is $\Phi =B_{\text{⊥}}A$ , the product of the area and the component of the magnetic field perpendicular to it.

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 an emf and what direction it takes depend on the change in $\Phi$ and how rapidly the change is made, as examined in the next section.

Test prep for ap courses

To produce current with a coil and bar magnet you can:

1. move the coil but not the magnet.
2. move the magnet but not the coil.
3. move either the coil or the magnet.
4. It is not possible to produce current.

(c)

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Section summary

• The crucial quantity in induction is magnetic flux $\Phi$ , defined to be $\Phi =\text{BA}\text{cos}\theta$ , where $B$ is the magnetic field strength over an area $A$ at an angle $\theta$ with the perpendicular to the area.
• Units of magnetic flux $\Phi$ are $\text{T}\cdot {\text{m}}^2$ .
• Any change in magnetic flux $\Phi$ induces an emf—the process is defined to be electromagnetic induction.

Conceptual questions

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

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Problems&Exercises

What is the value of the magnetic flux at coil 2 in [link] due to coil 1?

Zero

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