Physics 227: Lecture 12
RC Circuits, Magnetism
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Lecture 11 review:
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Resistors in series add: Req = R1 + R2 + ...
Resistors in parallel add inversely: 1/Req = 1/R1 + 1/R2 + ...
KCL: sum of currents into node (junction) = 0.
KVL: sum of voltages around loop = 0.
Ammeters, Voltmeters, and all that.
When is north south?
When it is the earth’s magnetic pole.
Monday, October 17, 2011
Changing current in a capacitor
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Two lectures ago we watched the current through a bulb change
as we charged and discharged a capacitor. How does this work?
For a capacitor, Q = CV.
But the current flow is a charge per unit time, so I = dQ/dt.
Thus: I = dQ/dt = d(CV)/dt = C dV/dt.
Monday, October 17, 2011
Changing current in a capacitor
• I = C dV/dt.
• At time t=0, close the switch.
• The voltage across the capacitor cannot
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``jump’’. dV/dt would be ∞, so there
would be ∞ power in the resistor!
Instead, Vab=ξ, I=ξ/R, and Vbc=0 at t=0+.
• The physics: the current flows charging the capacitor until V
at which point I = 0. No power is dissipated in the resistor.
Monday, October 17, 2011
bc
= ξ,
Changing current in a capacitor
• The physics: the current flows charging the capacitor until V
at which point I = 0. No power is dissipated in the resistor.
bc
= ξ,
• The math: From KCL: I = I ➭ V /R = C dV /dt.
• Rearrange & substitute: ξ - V = RC dV /dt.
• The solution: V = ξ ( 1 - e ) ➭ I = C dV /dt = (ξ/R) e
R
C
ab
bc
bc
-t/RC
bc
bc
-t/RC.
bc
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• Then dV /dt = (ξ/RC) e
• Substitute back in: ξ - V
The solution: Vbc = ξ ( 1 - e-t/RC).
bc
-t/RC.
bc
= RC dVbc/dt →
ξ - ξ ( 1 - e-t/RC) = RC (ξ/RC) e-t/RC
ξ e-t/RC = ξ e-t/RC
QED
Note: τ = RC has units of seconds. It is a time constant.
Monday, October 17, 2011
Capacitor iClicker
The switch is open and the
capacitor is charged to ξ.
Which of the following is true
immediately after the switch is
closed?
(You may ignore the signs of I and V.)
A. Vab = ξ.
B. Iab = 0.
C. Vbc = ξ/2.
D. Iab = ξ/RC.
E. Vbc = 0.
Monday, October 17, 2011
The voltage over the capacitor cannot jump,
and KVL requires Vab = Vbc = ξ. There are no
other elements in the circuit, so the two must
have equal magnitude voltages.
As a result, Iab = Vab/R = ξ/R.
Note that answer D has the wrong units: ξ/R
has units of current, so answer D has current
= current / capacitance.
Magnetism
Magnets are familiar.
Let’s have some demos and Phets.
Bar magnet and compass
Two magnets around hand, two clicking magnets
Monday, October 17, 2011
Magnetism Observations
Magnets have north and south
poles. Unlike poles attract (N+S),
like poles repel (N+N, S+S), similar
to charges.
Monday, October 17, 2011
Magnetism Observations
You never find a single pole alone.
This is unlike electric charges,
where you can find separate + and
- charges.
(No magnetic charge has ever
been observed, despite numerous
searches.)
Monday, October 17, 2011
What do field lines look like?
The magnet poles generate a
magnetic field that looks like the
electric field that would be
generated by charges in the same
positions as the poles.
Compass needles align to the
magnetic field - the field produces
a torque on the compass.
Demo! Phet! Magnetic field from
bar and horseshoe magnets, using
iron filings.
Monday, October 17, 2011
Magnetism and Currents
In the early 1800s Oersted
discovered that electrical currents
produce magnetic fields - a compass
needle is deflected by a current.
If there is a force from a current
on a magnet, there is a force from
a magnet on a current!
Monday, October 17, 2011
Magnetism iClicker
I am going to put a bar magnet (north pole) near a CRT tube - the
oscilloscope.
In what direction will the beam be deflected?
A. Up.
B. Down.
C. Your left.
D. Your right.
E. It will not be deflected.
We have the velocity (towards you)
crossed into (see next slides) the
magnetic field (downward) points to your
right, but the electron charge is
negative so the force on it is to your
left. As was shown in the lecture demo.
The demos: CRT and bar magnet,
TV and horseshoe magnet.
In what direction will the beam be deflected
if I put the south pole near the CRT?
Monday, October 17, 2011
Magnetic Force
The magnetic force is
perpendicular to the
directions of the
magnetic field and
the motion of the
charges. It is not
along the B-field line.
Monday, October 17, 2011
Magnetism and Currents
Observations:
The electric field is produced by electric charges, but
the magnetic field is produced by electric currents!
The E field exerts a force on charges - F = qE, while
the B field exerts a force on currents - but the magnetic
force is not in the direction of the magnetic field!
F = qE + qvxB. Recall the ``right-hand rule.’’
Note: a compass aligns to the field lines, but a moving charged
particle feels a force perpendicular to the field lines.
Monday, October 17, 2011
Magnetism and Currents
Faraday and Henry in the mid 1800s subsequently found moving
a magnet near a loop of wire leads to a current in it.
We will return to this point later.
Monday, October 17, 2011
Magnetism iClicker
What if I put the bar magnet (north pole) near the face of the
CRT tube - the oscilloscope?
In what direction will the beam be deflected?
A. Up.
B. Down.
C. Your left.
D. Your right.
E. It will not be deflected.
Monday, October 17, 2011
In the situation described the
electron velocity and the magnetic
filed are parallel, so the magnetic
force vanishes.
Thank you.
See you Thursday.
Monday, October 17, 2011