Lecture 12

Readings

http://umdberg.pbworks.com/w/page/50913084/Motivating%20simple%20electric%20models

http://umdberg.pbworks.com/w/page/73084742/A%20simple%20electric%20model%3A%20a%20line%20charge%20%282013%29

Line Charge , Electric Field

• Concept of linear charge density

• For example if $\lambda =\frac{3Coulombs}{1meter}$$\lambda = \frac{3\ Coulombs}{1\ meter}$ on a long cylinder ( a rod ) ( uniformly spread )

  • If I have a length of 1 meter of this rod, the total charge on the rod is Q = 3 Coulombs
  • If I have a length of 4 meters, the total charge on the rod is $Q=\lambda \ast 4=12Coulombs$$Q = \lambda * 4 = 12\ Coulombs$

  

  $$=\frac{3Coulombs}{1meter}\ast 4meters=12Coulombs$$
  $$=\frac{12Coulombs}{4meters}=\frac{3Coulombs}{1meter}$$

   

  • If the length of the subject is $\mathrm{\infty }$$\infin$ , I have $Q=\mathrm{\infty }$$Q = \infin$

    • But I still have $\lambda =\frac{3Coulombs}{1meter}$$\lambda = \frac{3\ Coulombs}{1\ meter}$ = a linear charge density

• We will soon also have an area of charge density which has units of $\frac{Coulombs}{meter{s}^2}$$\frac{Coulombs}{meters^2}$

• Electric Field

  • Direction

    

    • Directed straight away in all directions, so it's 3-dimensional ( like bottle brush )

    • Readings discussed why this is true.

      • Its due to cancellation of any Electric Field that might point to the left or right

• Magnitude

  • Gets weaker as you get farther away
  • Specifically:
  $$|\stackrel{\rightharpoonup }{E}|=\frac{2\ast k_c\ast \lambda }{d}$$
  • d is (perpendicular) distance from the line
  • $|\stackrel{\rightharpoonup }{E}|$$|\overset{\rightharpoonup}{E}|$ increases if $\lambda$$\lambda$ increases
  • $|\stackrel{\rightharpoonup }{E}|$$|\overset{\rightharpoonup}{E}|$ decreases if $d$$d$ increases

  

   

  • Compare this equation to that for a point charge:
  $$|\stackrel{\rightharpoonup }{E}|=\frac{k_c\ast q}{r^2}$$

  • Notice that point charge falls of as $r^2$$r^2$ , but line charge only falls off as $d$$d$ ( no squared in denominator).

    • So that $E$$E$ field from a point charge gets smaller faster

Clicker Questions