Figure 20.9 Loop of wire in the plane of a magnetic field.No field lines go through the loop. Rather, they all hit the edge of the loop, but none of them actually
passes through the center of the loop. So we know that our flux should equal zero.
Okay, this time we will orient the field lines so that they pass through the middle of the loop. We’ll
also specify the loop’s radius = 0.2 m, and that the magnetic field is that of the Earth, B = 5 × 10−5 T. This
situation is shown in Figure 20.10 .
Figure 20.10 Loop of wire with magnetic field lines going through it.Now all of the area of the loop is penetrated by the magnetic field, so A in the flux formula is just the area
of the circle, πr 2 .
The flux here is
Φ (^) B = (5 × 10−5 )(π) (0.2^2 ) = 6.2 × 10−6 T·m^2 .
Sometimes you’ll see the flux equation written as BA cosθ . The additional cosine term is only relevant
when a magnetic field penetrates a wire loop at some angle that’s not 90°. The angle θ is measured
between the magnetic field and the “normal” to the loop of wire ... if you didn’t get that last statement,
don’t worry about it. Rather, know that the cosine term goes to 1 when the magnetic field penetrates
directly into the loop, and the cosine term goes to zero when the magnetic field can’t penetrate the loop at
all.
Because a loop will only “feel” a changing magnetic field if some of the field lines pass through the
loop, we can more accurately say the following: A changing magnetic flux creates an induced EMF .
Faraday’s law tells us exactly how much EMF is induced by a changing magnetic flux.