Electricity and Magnetism

1
Electricity and Magnetism
Physics 208
Dr. Tatiana Erukhimova
Lectures 20 - 21
2
Current Density
Consider current flowing in a homogeneous wire
with cross sectional area A.
3
The Continuity Equation for Steady State Currents
Currents and current densities are constant in
time steady state. The flux of out of any
closed surface must be zero.
4
Another form of Ohms Law
5
For steady state situation
6

• Problem 4
• Two wires having different resistivities ?1 and
  ?2 and equal cross sections, a, are connected end
  to end. Their lengths are l1 and l2. If a
  battery is connected to this system such that a
  potential difference of V is maintained between
  the ends,
• What will be the current densities in the wires?
• What will be the potential difference across
  each wire?
• Will there be any charge on the surface where the
  wires are connected?

7
Exercise 5
Consider a cylindrical shell, inner radius a and
outer radius b. It is made of material with
resistivity ?. Suppose a current can be made to
flow out from the inner surface to the outer.
What would the resistance be for this current?
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Resistivity and temperature
Metal ? increases with increasing T
9
Semiconductors ? decreases with increasing T
10
Superconductor
1911 Dutch physicist Heike Kamerlingh Onnes -
Hg
2003
Once a current has been established in a
superconducting ring, it continues indefinitely
without the presence of any driving field.
11
Water
Nitrogen
Oxygen
Gas
100 C (212 F)
-196 C (-322 F)
-183 C (-297 F)
Boils
Liquid
0 C (32 F)
-223 C (-369 F)
Freezes
-210 C (-346 F)
Solid
Our air is ¾ Nitrogen and ¼ Oxygen
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Superconductivity

• 1908- liquefied helium produced
• First discovered in mercury by Kamerlingh-Onnes
  in 1911.
• Critical temperature 4.21K.
• Nobel Prize in 1913.

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High-Tc Superconductivity
Complex ceramic materials were discovered in
1986. They exhibit superconductivity at much
higher temperatures above LN temperature! Mulle
r and Bednortz, Nobel Prize 1987
Liquid nitrogen temperature 77 K
14
Meissner effect and magnetic levitation
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For steady state situation

1. Kirchhoffs junction rule The algebraic sum of
   the currents into any junction is zero.
2. Kirchhoffs loop rule The algebraic sum of the
   potential differences in any loop must be zero.

16
Resistors in series
Resistors in parallel
17
Circuit with capacitors