# PHYS 1B Lecture Notes - Lecture 6: Field Line, Electric Field, Surface Charge

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1/27/17
- For a single charge q, E = ke (q/r^2)r
o If multiple charges, the total electric field is the vector sum of the fields produced by
each charge qi where I = ,,…
- Clicker question: A positive charge q is located a distance d from a 2nd identical charge.
Is the electric field zero anywhere?
o YES, located in between the 2 charges
o What if there was one positive ad one negative charge?
YES, located on the outside of the charges
- Electric field of a dipole
o Electric dipole: consists of 2 point charges q and q separated by distance 2a
o Neutral atoms and molecules behave as dipoles when placed in an external electric
field (due to polarization)
o Some molecules (HCl) also permanent dipoles (H+ and Cl-)
o For r >> a, you find that E = ke(2qa/r^3)
Contrasts with a single charge
- Electric field lines
o Field lines represent the electric field pictorially
o BY DEFINITION: the lines point in the direction of the electric field vector at every
point in space
o The number of lines passing through a unit surface area perpendicular to the lines is
proportional to the magnitude of the electric field in that region
o Rules for drawing electric field lines:
Lines begin on positive charge and end on negative charge
If excess of one type of charge, some lines will begin/end infinitely far away
The number of lines drawn leaving the positive charge or approaching the
negative charge is proportional to the magnitude of the charge
2 field lines never cross
o ex of 2 equal positive charges:
same number of lines leave each charge since they are equal in magnitude
at great distance, field is 2q
o ex of 2 charges +2q and q
2 lines leave positive charge for each line that terminates on the negative charge
at great distance, field is q
- Continuous charge distributions
o Divide charged objects into small elements, each of which contains charge delta(q)
o Total field is the sum of fields due to each element
o Take the limit to change the sum to an integral
o *don’t actually need to do integral calculations
- Uniformly charged sphere (insulator)
o Charge q evenly distributed over the volume of sphere of radius a (must be an
insulator, or else charges would move and not be evenly distributed)
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