Download ☺ PLAN 1. Ampere’s law 2. Applications

PLAN
1. Ampere’s law
2. Applications Require a high symmetry.
♣ Magnetic field due to i in a long straight
wire — again. (Faster. No need to
assume that the wire diameter is zero.)
♣ Magnetic field inside the wire.
♣ Solenoid.
♣ Toroid.
☺
3. Magnetic field of a single coil. (Only along
the symmetry axis. But you need to use
the Biot-Savart law.)
Electricity vs Magnetism
Electricity
Coulomb’s law Ù Gauss’ law
Magnetism
Biot-Savart law Ù Ampere’s law
r
r r
Plus: FB = qv × B
Ampere’s Law
• Take arbitrary path around set of currents
– Let ienc be total enclosed current (+ up, − down)
– Let B be magnetic field, and ds be differential length
along path (couterclockwise according to the right
hand rule)
Not included in ienc
• Only currents inside path contribute!
– 5 currents inside path (included)
– 1 outside path (not included)
r
ds
θ
r
B
Check Point
Q1 Which of the three loops has the
largest magnitude of Amperian integral? d
Q2 The smallest?
b
Example 2: Inside the Wire
• Find B vs r inside long wire, assuming uniform
current
R
r
Example 3: Solenoid
Loosely wound and short
Tightly wound and long
(~infinitely long)