Introductory Physics Volume Two

28 Electric Field 1.7
Determine what the other two charges in the previous example do when the
leftmost charge is moved to the left.
They accelerate towards each other
⊙ Do This Now 1.6
An electron accelerates east due to an electric field. What direction does the
electric field point?
west
Example
A dust particle with mass 2µg has a net electric charge 3µC. The
piece of dust is in a region of uniform electric field and is observed to
accelerate at a rate of 180 m s 2 . What is the magnitude of the electric
field in that region of space?
The net force on the dust particle can be computed using Newton’s
second law:
F net = (2 × 10 −9 kg)(180 m s 2 ) = 3.6 × 10 −7 N.
Using the definition of electric field and assuming no other forces act
on the dust particle:
E = F q = 3.6 × 10−7 N
3 × 10 −6 C = 0.12 N C .
Example
If a proton is placed in the same electric field from the previous example,
what is the resulting acceleration?
Work backwards:
F = qE = (1.6 × 10 −19 C)(0.12N/C) = 1.9 × 10 −20 N
a = F m =
1.9 × 10−20 N
1.67 × 10 −27 kg = 1.15 × 107 m s 2
Example
Three charges lie along a line as shown below. What is the electric
field at a position that is a horizontal distance a to the right of the −q
charge?
-4q +2q -q
2a
a
Here is a diagram indicating the electric field due to each charge at the
point: