Maxwell

1
Maxwells Equations

• PH 203
• Professor Lee Carkner
• Lecture 25

2
Transforming Voltage

• We often only have a single source of emf
• We need a device to transform the voltage
• Note that the flux must be changing, and thus the
  current must be changing
• Transformers only work for AC current

3
Basic Transformer

• The emf then only depends on the number of turns
  in each
• e N(DF/Dt)
• Vp/Vs Np/Ns
• Where p and s are the primary and secondary
  solenoids

4
Transformers and Current

• If Np gt Ns, voltage decreases (is stepped down)
• Energy is conserved in a transformer so
• IpVp IsVs
• Decrease V, increase I

5
Transformer Applications

• Voltage is stepped up for transmission
• Since P I2R a small current is best for
  transmission wires
• Power pole transformers step the voltage down for
  household use to 120 or 240 V

6
Maxwells Equations

• In 1864 James Clerk Maxwell presented to the
  Royal Society a series of equations that unified
  electricity and magnetism and light
• ? E ds -dFB/dt
• ? B ds m0e0(dFE/dt) m0ienc
• ? E dA qenc/e0
• Gausss Law for Magnetism
• ? B dA 0

7
Faradays Law

• ? E ds -dFB/dt
• A changing magnetic field induces a current
• Note that for a uniform E over a uniform path, ?
  E ds Es

8
Ampere-Maxwell Law

• ? B ds m0e0(dFE/dt) m0ienc
• The second term (m0ienc) is Amperes law
• The first term (m0e0(dFE/dt)) is Maxwells Law of
  Induction
• So the total law means
• Magnetic fields are produced by changing electric
  flux or currents

9
Displacement Current

• We can think of the changing flux term as being
  like a virtual current, called the displacement
  current, id
• id e0(dFE/dt)
• ? B ds m0id m0ienc

10
Displacement Current in Capacitor

• So then dFE/dt A dE/dt or
• id e0A(dE/dt)
• which is equal to the real current charging the
  capacitor

11
Displacement Current and RHR

• We can also use the direction of the displacement
  current and the right hand rule to get the
  direction of the magnetic field
• Circular around the capacitor axis
• Same as the charging current

12
Gausss Law for Electricity

• ? E dA qenc/e0
• The amount of electric force depends on the
  amount and sign of the charge
• Note that for a uniform E over a uniform area, ?
  E dA EA

13
Gausss Law for Magnetism

• ? B dA 0
• The magnetic flux through a surface is always
  zero
• Since magnetic fields are always dipolar

14
Next Time

• Read 32.6-32.11
• Problems Ch 32, P 32, 37, 44

15

• How would you change R, C and w to increase the
  rms current through a RC circuit?
• Increase all three
• Increase R and C, decrease w
• Decrease R, increase C and w
• Decrease R and w, increase C
• Decrease all three

16

• How would you change R, L and w to increase the
  rms current through a RL circuit?
• Increase all three
• Increase R and L, decrease w
• Decrease R, increase L and w
• Decrease R and w, increase L
• Decrease all three

17

• How would you change R, L, C and w to increase
  the rms current through a RLC circuit?
• Increase all four
• Decrease w and C, increase R and L
• Decrease R and L, increase C and w
• Decrease R and w, increase L and C
• None of the above would always increase current