ELECTRIC FIELD (Section 19.5)
Electric fields due to point charges for now (will do more later)
Imagine an arrangement of point
charges in space
Force on a small positive charge q3 at P
Force on a small negative charge q4 at P
Don’t need a different vector sum for each different charge at P!
Force on a small positive charge q3 at P
Force on a small negative charge q4 at P
Define ELECTRIC FIELD at P:


F3 F4 

 Eat P
q3 q 4
 Charges q1 and q2 cause an electric field at P
 The electric field at P is independent of charge at P
ELECTRIC FIELDS: IMPORTANT CONCEPTS
 Any point charge q creates an electric field at all surrounding points in space

 If the electric field at a point in space is E , then the force on a charge q0 at


that point is F  q0 E


o F is in the same direction as E for positive q0


o F is in the opposite direction from E for negative q0

q
 If the electric force on a charge 0 at a point in space is known to be F

 F
o then the electric field at that point must be E  q
0
o The units of electric field are N/C
 Force and Electric Field are both VECTORS
Direction for Force and Electric Field: another special unit vector r̂
For the ELECTRIC FORCE on a charge at P due to a charge q:
 Unit vector r̂ points from q → P

qq0
F

k
rˆ
e
2
 Force is qq0
r
o Points in same direction as r̂ if q and q0 have the same sign
o Points in opposite direction to r̂ if q and q0 have opposite signs
For the ELECTRIC FIELD at P due to a charge q:

Fqq0

q
ˆ
E


k
e 2 r
 Electric field at P is P
q0
r

o Points in same direction as r̂ if q is positive ( E points away from +)

q
r̂
o Points in opposite direction to if is negative ( E points toward -)
Superposition:
Because Electric Field is a vector:

 The total E at any point P due to a particular arrangement of point charges
is the VECTOR SUM of the electric field vectors due to all charges around P
 Total electric field at P is:





q rˆ
ET  k e  i 2 i  E1  E2  E3  E4
ri
i
o q i is the charge at i
o ri is the distance from q i → P
o r̂i is the unit vector from q i → P
o the sum is a VECTOR SUM
The Electric Dipole is an important arrangement of charges
 charges  q and  q separated by distance 2a
o Charges in some molecules (polarizable) separate in an electric field
 Result is an induced electric dipole
 responsible for van der Waal’s interaction
o Many molecules have permanent electric dipoles (i.e. water)
o Insulators in which dipoles can be induced are used in capacitors
 dielectrics
Example:
(a) Show that the electric field at point P a distance y above
the midpoint of an electric dipole aligned along the x-axis
is:

2k e q a ˆ
EP 
i
2
2 3/ 2
a y


(b) Show that the electric field at point P a distance
x along the x-axis from the midpoint of an
electric dipole aligned along the x-axis is:

 1
1 ˆ

EP  ke q 
i
2
2
 x  a  x  a  
(c) Using
1  x n  1  nx  nn  1 x 2   , show that for
part (b) becomes
2

4k q a
E P   e3 iˆ
x
x>>a the answer in
For point charges:
 calculate contributions to total electric field at a point in space from each
point charge separately
o then find total electric field by doing a vector sum.
For a continuous charge distribution (i.e. a line of charge, a charged surface,
or a charged volume)
 Break charge distribution into small elements
o treat each element as a point charge.
 Write a vector sum of contributions from all elements
 Take limit as elements become infinitesimally small
o Sum becomes an INTEGRAL! (but don’t panic. You will be shown how
to evaluate)
We will come back to do electric fields due to continuous charge
distributions later!