Download Week 10 Thursday

Lecture 3/23/2017
• Review DC Circuits
• Introduction to Magnetism
Circuits Containing Resistor and Capacitor (RC
Circuits)
In the circuit shown, the capacitor is originally
uncharged. Describe the behavior of the lightbulb
from the instant switch S is closed until a long time
later.
a)The bulb is on and remains with
equal brightness over time.
b)The lightbulb is initially
off but it gets brighter over
time.
c)The bulb is initially bright
but it dims over time and
eventually is dark.
What happens to the voltage
1) increase
across the resistor R1 when the
2) decrease
switch is closed? The voltage will:
3) stay the same
R1
S
R3
V
R2
Find the currents I1 ( through the 10V
battery), I2 (through the 14V battery), I3
(through the 2Ω resistor) in the circuit.
𝑰𝟏 + 𝑰𝟐 = 𝑰𝟑
𝟏𝟎. 𝟎 − 𝟔. 𝟎𝑰𝟏 − 𝟐. 𝟎𝑰𝟑 = 𝟎
−𝟏𝟒. 𝟎 + 𝟔. 𝟎𝑰𝟏 − 𝟏𝟎. 𝟎 − 𝟒. 𝟎𝑰𝟐 = 𝟎
𝑰𝟏 = 𝟐. 𝟎𝑨
𝑰𝟐 = −𝟑. 𝟎𝑨
𝑰𝟑 = −𝟏. 𝟎𝑨
The switch S has been open for a long time. It
is then suddenly closed. Determine the
time constant before the switch is closed.
Time constant
𝝉 = 𝑹𝑪 = 𝟏. 𝟓𝒔
The switch S has been open for a long time. It
is then suddenly closed. Determine the
time constant after the switch is closed.
Time constant
𝝉 = 𝑹𝑪 = 𝟏𝒔
The switch S has been open for a long time. It
is then suddenly closed. Determine the
current in the switch as a function of time.
𝐼𝑆 = 𝐼𝑏𝑎𝑡𝑡𝑒𝑟𝑦 + 𝐼𝑐𝑎𝑝𝑎𝑐𝑖𝑡𝑜𝑟
𝐼𝑐𝑎𝑝
𝑄𝑜 −𝑡/𝑅𝐶
𝑡 =
𝑒
𝑅𝐶
𝐼𝑏𝑎𝑡𝑡𝑒𝑟𝑦
𝑉
= = 200𝜇𝐴
𝑅
𝐼𝑐𝑎𝑝 𝑡 = 100𝜇𝐴 𝑒 −𝑡
𝐼𝑆 (𝑡) = 200𝜇𝐴 + 100𝜇𝐴 𝑒 −𝑡
𝑰𝑺 (𝟏𝒔) = 𝟐𝟑𝟕𝝁𝑨
Magnets and Magnetic Fields
Magnets have two ends – poles – called north
and south.
Like poles repel; unlike poles attract.
Magnets and Magnetic Fields
If you cut a magnet in half, you don’t get a
north pole and a south pole – you get two
smaller magnets.
Magnets and Magnetic Fields
Magnetic fields can be visualized using
magnetic field lines, which are always closed
loops.
Magnets and Magnetic Fields
The Earth’s magnetic field is similar to that of a
bar magnet.
Note that the Earth’s
“North Pole” is really
a south magnetic
pole, as the north
ends of magnets are
attracted to it.
Magnets and Magnetic Fields
The field between
these two wide poles
is nearly uniform.
A uniform magnetic field is constant in
magnitude and direction.
Electric Currents Produce Magnetic Fields
Experiment shows that an electric current
produces a magnetic field.
The direction of the field is given by a righthand rule.
Electric Currents Produce Magnetic Fields
Here we see the
field due to a
current loop;
the direction is
again given by
a right-hand
rule.
Force on an Electric Current in a Magnetic Field;
Definition of 𝑩B
A magnet exerts a force on
a current-carrying wire.
The direction of the force is
given by a right-hand rule.
Force on an Electric Current in a Magnetic Field;
Definition of 𝑩 B
The force on the wire depends on:
- the current,
- the length of the wire,
- the magnetic field, and its orientation.
This equation defines the magnetic field 𝑩.
In vector notation:
Arbitrarily Shaped Wire
It follows from 𝑭 = 𝑰ℓ × 𝑩 that the magnetic
force exerted on a small segment of vector
length 𝐝𝒔 in the presence of a magnetic field 𝑩
is:
𝒅𝑭 = 𝑰𝒅𝒔 × 𝑩
𝒃
→
𝑭 = 𝑰 න 𝒅𝒔 × 𝑩
𝒂
Example: Arbitrarily Shaped Wire
𝒃
𝑭 = 𝑰 න 𝒅𝒔 × 𝑩
𝒂
Case1. A curved wire carrying a current I in a
uniform magnetic field of magnitude B.
Case 2. A closed loop of wire carrying a current I
in a uniform magnetic field of magnitude B.
Example: Arbitrarily Shaped Wire
𝒃
𝑭 = 𝑰 න 𝒅𝒔 × 𝑩
𝒂
Case1. A curved wire carrying a current I in a
uniform magnetic field of magnitude B.
Example: Arbitrarily Shaped Wire
𝒃
𝑭 = 𝑰 න 𝒅𝒔 × 𝑩
𝒂
Case 2. A closed loop of wire carrying a current I
in a uniform magnetic field of magnitude B.
Force on an Electric Current in a Magnetic Field;
Definition of 𝑩 B
Unit of B: the tesla, T:
1 T = 1 N/A·m.
Another unit sometimes used: the gauss (G):
1 G = 10-4 T.
1) + x
A rectangular current loop is
2) + y
in a uniform magnetic field.
3) zero
What is the direction of the
4) - x
net force on the loop?
5) - y
B
z
y
x
Force on an Electric Charge Moving in a
Magnetic Field
The force on a moving charge is related to
the force on a current:
Once again, the
direction is given by
a right-hand rule.