CK-12-Physics - Intermediate

http://www.ck12.org Chapter 19. Electromagnetism

Both of the above experiments confirm that:

• A current may be produced by a changing magnetic field.


• A voltage may be produced by a changing magnetic field.

These phenomena are typically calledelectromagnetic induction.
http://www.youtube.com/watch?v=wGfVVGjGVB8&feature=related
Faraday realized that the rate at which the magnetic field changed would have an effect on the induced voltage. He
also realized that the number of lines of magnetic force which crossed the coil (or loop) also needed to be taken into
consideration.
In order to calculate the number of field lines that pass through a loop, we define a new term called an area vector
~A, as shown inFigure19.4. The area vector has the magnitude equal to the area enclosed by the loop (or any other

enclosed surface) and the direction perpendicular (normal) to the plane of the loop (or surface).

We will use the term flux to describe the number of magnetic field lines that pass through a surface.

FIGURE 19.4

Area vector.

The product of the magnitude of the magnetic field vector~B, the magnitude of the area vector~A, and the cosine of

the angleθbetween them, is called themagnetic flux, represented with the Greek letter phi(Φ), as shown inFigure

19.4.

Φ=BAcosθ

For an interactive activity involving magnetic flux,follow the link below.

http://demonstrations.wolfram.com/MagneticFluxThroughALoopOfWire/

We can see from the definition of the flux that the units of flux areT∗m^2.

The unit of flux is called the weber, for the German physicist Wilhelm E. Weber (1804-1891),Figure19.5.

1 T∗m^2 = 1 W b

Figure19.6 (a) shows the maximum number of magnetic field lines passing through a loopLwhenθ= 0 ◦.

The flux isΦa=BAcos 0◦=BA.

At point (b) the loop is rotated 45◦and the number of field lines passing through the loop is smaller than in (a).

The flux isΦb=BAcos 45◦= 0. 707 BA.

And at point C the loop is rotated 90◦, and the number of field lines passing through the loop is zero.

The flux isΦc=BAcos 90◦=0.