Lecture 13

Readings

http://umdberg.pbworks.com/w/page/73084823/A%20simple%20electric%20model%3A%20a%20sheet%20of%20charge%20%282013%29

http://umdberg.pbworks.com/w/page/63914637/Two%20parallel%20sheets%20of%20charge%20%282013%29

Electric Field of an Infinite Plane of Charge

• Direction is straight away (if positively charged) and straight towards (if negatively charged)

• It won't point sideways

• Because, how would it choose which direction sideways? Symmetry says it won't happen

Magnitude

• Where $\sigma$$\sigma$ is the surface charge density, $\frac{Coulombs}{meter{s}^2}$$\frac{Coulombs}{meters^2}$

• Doesn't depend on distance from plane at all!

• How can this be?

  • How does an infinite plane look if you are 1 mm away?
  • 1 m away?
  • 1000 m away?
  • ${10}^6$$10^6$ m away?

• Always the same, like an infinite plane

Capacitors

• $|\stackrel{\rightharpoonup }{E}|$$|\overset{\rightharpoonup}{E}|$ between the plates = sum of $\stackrel{\rightharpoonup }{E}$$\overset{\rightharpoonup}{E}$ from each sheet

• If charges are the same magnitude, but opposite sign , $\sigma$$\sigma$ and $-\sigma$$-\sigma$ (the usual case) , then $|\stackrel{\rightharpoonup }{E}|=4\ast \pi \ast k_c\ast \sigma$$|\overset{\rightharpoonup}{E}| = 4 * \pi * k_c * \sigma$

  • Twice what it was for a single plate of charge

• How close is "close enough" ? (finite plates)

  • No real rule

  • Roughly, each dimension of area should be about 10 times the separation.

    • For example, if separation = $d=10nm$$d = 10\ nm$ , then the plates should be more than $100nm\ast 100nm$$100\ nm * 100\ nm$

  • The closer you are to the middle of the area, the better the "infinite plate" assumption is:

Clicker Questions