Name:_________________________________
Section:_________
Physics 208 Group Problem
Your credit card is magnetized with your account information as shown below. It slides
past a pick-up coil in a card swipe as shown below. The magnitude of the magnetic field
is 0.1T. The track is encoded at 72 bits per inch, so the field can change abruptly about
every 0.40 mm. The pick-up coil is 0.20mm X 0.20mm square, with 1000 turns of wire.
0.2mm X 0.2mm
1000 turn coil
Slide card to left at
constant speed
Time t=0
0.4m
m
Field changes here
between into page
and out of page.
Credit card
magnetic stripe
a) At what instant in time is the magnitude of the EMF induced in the coil the largest?
The card moves to the left at constant speed at all times.
Circle the correct answer(s).
A.
B.
C.
D.
In B and D, the flux is constant when the card slides, since the field is uniform. In A,
the entering flux replaces zero flux. In C, the entering flux replaces the oppositelyoriented flux. So EMF=-dΦ/dt is twice as large in C as in A.
Name:_________________________________
Section:_________
b) Plot the flux through the loop as a function of time, and plot the induced EMF as a
function of time.
Field into the page produces a positive flux through the loop,
and an EMF producing a clockwise current is defined as positive.
Your plots should start at t=0 as defined in the figure on the previous page.
flux
0
time
EMF
0
time
c) Suppose the coil needs at least 1mV (10-3V) of EMF in order to read your card. What
is the minimum speed at which you can slide the card so that the peak EMF around
the coil is 1mV?
Calculate EMF=-dΦ/dt.
Look at position C in part a). The flux at this position is zero. When the loop moves half its
diameter (=0.1mm), it just arrives entirely in the into-page field region, and has a flux of
(0.1T )(2 ×10−4 m × 2 ×10−4 m) = 4 ×10−9 Wb through a single turn.
If this motion took 1 s (a speed of 0.01cm/s) this would be a flux rate of change of 4x10-9Wb/s
through a single turn, producing an EMF of 4x10-6V around 1000 turns.
To get 1 mV, the speed needs to be 10−3 V /4 ×10−6 V = 250 times larger, or 2.5 cm/s
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