Lecture 11

Readings

http://umdberg.pbworks.com/w/page/63757839/The%20electric%20potential%20%282013%29

Electric Potential

• For a single charge, $V=\frac{k_C\ast q}{r}$$V = \frac{k_C * q}{r}$

• $V$$V$ is very large and positive when near a positive charge

• $V$$V$ is very small ( still positive ) when far from a positive charge

• $V$$V$ is very large and negative when near a negative charge

• $V$$V$ is very small ( still negative ) when far from a negative charge

• Notice, there are no vectors in this equation.

  • There is no "direction" to electric potential

• If the system has multiple charges, find total $V$$V$ at a point in space by adding up values of $V$$V$ due to each charge

• 4 electric quantities in a 2x2 arrangement ( point charges ):

• We've seen this relationship between potential energy (top left) and force (top right) before
• The (negative) slope of potential energy graph gives us the force magnitude and direction
• Not that Electric potential (bottom left) is not the same as potential energy (top left)
• Plot of $V$$V$ along x-axis for a single positive charge at origin:

• Slope is negative, so force on a positive charge ( a different positive charge than the one at the origin ) is to the right ( ball "rolls" that way )
• Bigger force for smaller x , because steeper slope

• All of the preceding was for a point charge
• For other arrangements of charge, $V$$V$ and $E$$E$ will be different formulas
• Very common case is $V$$V$ is linear in some dimension, say x

• If you know $V_2-V_1$$V_2-V_1$ between 2 points $x_2$$x_2$ and $x_1$$x_1$ , you can find $|\stackrel{\rightharpoonup }{E}|$$|\overset{⇀}{E}|$ from the slope

  • This will be used for "capacitors" and biological membranes