Download Science One Physics Lecture 10 Circuits => Magnetism

Science One Physics
Lecture 10
Circuits => Magnetism
Clicker[Q]
We close the switch. What is the voltage across the capacitor
once the circuit has run for a while?
(a) 0V, (b) 12V, (c) 40V, (d) 60V,
(e) depends on the capacitance
Clicker[Q]
We close the switch. What is the voltage across the capacitor
once the circuit has run for a while?
(a) 0V, (b) 12V, (c) 40V , (d) 60V,
(e) depends on the capacitance
1820: Electricity and magnetism are linked!
Magnetic fields
v
e
moving electron reacts
to magnetic field
at its location
moving electron
generates a magnetic field
in all of space
F
e
v
Magnetic field and force
moving charge q
magnetic dipole m
field
force/energy
µ0 q v × r̂
4π r2
Biot-Savart law
F = qv×B
Lorentz force
µ0
B=
(3(mr̂)r̂ − m)
4πr3
magnetic field of dipole
E = −mB
B=
Clicker[Q]
Clicker[Q]
Clicker[Q]
Clicker[Q]
[Q]
[Q]
[Q]
How can we determine the strength
and direction of a magnetic field?
Strength and direction of a magnetic field
[Q]
How can we characterize the strength of a
magnet?
What is the magnetic counterpart to electric
charge?
Characterization of magnets
How can we characterize the strength of a magnet?
What is the magnetic counterpart to electric charge?
• For magnets, orientation matters
⇒ Magnets are characterized by a vector-valued quantity, the
magnetic dipole moment m.
Clicker[Q]
Clicker[Q]
Magnetic field and force
moving charge q
magnetic dipole m
field
force/energy
µ0 q v × r̂
4π r2
Biot-Savart law
F = qv×B
Lorentz force
µ0
B=
(3(mr̂)r̂ − m)
4πr3
magnetic field of dipole
E = −mB
B=
Clicker[Q]
Clicker[Q]
Field of a magnet
m: strength & orientation of magnet (magnetic dipole moment)
r: vector from center of magnet to probe location
B=
µ0 (mr̂)r̂ − m
4π
r3
Along the axis of the magnet, m||r,
µ0 2|m|
|B| =
.
4π r3
A magnet in a magnetic field
m0: magnetic dipole moment of second magnet
B: magnetic field
The energy E of the second magnet in the field B is
E = −m0B
Biot-Savart law – B-field of a moving charge
Biot-Savart law – B-field of a moving charge
µ0 qv sin θ
B=
4π r2
B =
µ0 q v × r̂
4π r2