Electric Fields
The earth is surrounded by a gravitational field, which means that any object with mass will have a force
exerted on it by the earth’s gravity. Earth’s gravitational force is easily noticeable, but, because gravity is so
weak, we rarely notice the attraction between everyday objects.
This is not true for electric charges. A group of them exert significant forces on each other that cannot be
ignored. An appropriate analogy would be the interaction of a few planets crammed into a volume one onethousandth that of our solar system.
An electric field exists around any charged object in space. A second charged object brought into this field
experiences force according to Coulomb's law. The electric field E is a vector quantity. The direction of the
field is the direction a positive would be pushed.
In these drawings, Q represents the charge causing the field and q represents a “test charge” which is positive.
Here, a positive charge Q exerts a force on a test charge q.
The direction of the force is away from Q.
With the test charge at a new location,
the force exerted has a new direction,
but it is still away from Q.
We represent the field and the direction of the forces it will exert by drawing lines.
These lines show what a test charge would feel.
These are called electric lines of force.
Electric lines of force: lines drawn so that a tangent to the lines shows the direction of electric force
The drawing of field lines requires following a few simple rules.
1. The number of lines per unit area is proportional to the strength of the field.
2. Where E (the electric field strength) is large, the lines will be close together.
Where E is small, the lines will be far apart.
3. The field around a positive charge is represented with arrows pointing away.
4. The field around a negative charge is represented with arrows pointing toward.
The field around a positive charge would look like this. Notice that there are 8 lines
radiating from the charge. They are also evenly spaced. A positive charge placed
anywhere near the big charge would feel pushed away.
The lines of force around a negative charge would look like this if the charge were
half as strong. Note that there are only 4 lines this time. A positive charge placed
anywhere near the big charge would feel pulled in.
Lines of force between two like charges
Lines of force between two unlike charges
Field Intensity: a measure of the field’s strength, represented by the symbol E. The field intensity shows
how much force a Coulomb of charge would feel at a particular point.
E=F/q
E represents field intensity, F represents force, q represents the test charge.
The test charge, q, is not the charge that made the field!
q0 is a test charge that is in the field made by Q.
The unit for field intensity is a Newton per Coulomb.
Exercise: An electric field has a field intensity of 2•104 N/C.
The force acting on a test charge is 6.2 N.
What is the magnitude of the test charge?
E=F/q
q=F/E
q = 6.2N / 2•104 N/C
q = 3.1•10-4C
Once one knows the forces, Newton’s laws can calculate velocity or acceleration.
Exercise: An electron enters a uniform electric field.
(a) What is the direction of the force acting on the electron?
(b) What is the magnitude of the force?
(c) What is the acceleration acting on the electron?
(d) how much time would it take the electron to travel 3mm?
(e) If the electron travels a distance of 3mm in the field,
how far will it be deflected from its original path?
(a) The field lines show what a positive charge would feel.
A negative electron would be pushed down.
(b)
E=F/q
F = qE
F = (1.6•10-19C) (280 N/C)
F = 4.5•10-17 N
(c)
F = ma
a=F/m
a = 4.5•10-17 N / 9.11•10-31 kg
a = 4.9•1013 m/s2
(d)
d = Vt
t=d/v
t = 0.003m / 2.35•105m/s
t = 1.3•10-8s
(e)
∆y = ½ a t2
∆y = ½ (4.9•1013 m/s2) (1.3•10-8s)2
∆y = 0.0041m
Electric Fields and Objects: The electric charge on an object is always on the outside of the object. The
free electrons repel each other, meaning they try to get as far away from each other as possible. To do this,
they collect on the outside surface and spread out. If they were on the inside, they would be closer together.