Faraday's
Law
Faraday’s Law, Eq.1, relates the emf in the coil to
the rate that the flux through the coil changes in time. By integrating
Faraday's Law, we can find the total change in flux,
ΔΦ (Delta Phi), through the coil. Since
flux represents the number of magnetic field lines passing through the
coil,
ΔΦ (Delta Phi) is just the final number of
field lines minus the initial number of field lines passing through the
coil. The computer produces a plot of the emf as a function of time, so the integral in Eq. 2
is just the total area under the curve. When the magnet is far from the coil, the flux
through the coil is negligibly small. When the magnet reaches the
midpoint of the coil, all of the field lines leaving the north pole (or
coming into the south pole) of the magnet pass through the coil. At this
point the flux has reached its maximum value. For an instant, the flux
through the coil remains constant, so no emf is produced, and the graph
crosses the x-axis. (Remember that the flux is the integral of the emf
curve, so be careful not to confuse the point where the flux is largest
and the point where the emf is largest!) Then as the magnet
continues to fall through the loop, the emf reverses and the the total
change in flux - the area under the curve - decreases until it
eventually becomes zero. (Initially there was no flux through the coil. At
the end of the experiment, there was no flux through the coil. The net
change in number of field lines is then 0-0=0, so
ΔΦ(Delta Phi=0)).
Eq. 9.1
Eq. 9.2
1.
Obtain a printout of
ε(t), the emf as a
function of time. Note the position on
the graph that corresponds to the midpoint of the coil. The emf will pass
rapidly through zero at this position.
Manually integrate the number of grid squares under the curve prior
to this point.
Number of squares =
2.
Calculate the change in magnetic flux represented by one grid
square:
Eq. 9.3
In this equation
Δε (Delta emf) represents the distance
between lines on the y axis in volts, and
Δt (Delta t) represents the distance
between lines on the x axis in seconds. (We ignore the minus sign,
as it only indicates direction.)
Change in flux for one square =
Wb
4.
Multiply this value by the number of squares obtained in
Step 1 to get the total magnetic flux of the magnet. (The change in flux
to the point that the magnet is midway in the coil is total flux of the
magnet.)
Total flux of the magnet:
Wb
5.
Assuming that the magnetic field inside the magnet is uniformly
distributed over its 5mm radius, calculate the magnitude of the magnetic
field inside the magnet. (Remember that flux is BA.)
Magnetic field strength:
T
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