The electric field is thus seen to depend only on the charge
and the distance
; it is completely independent of the test charge
.
Calculating the electric field of a point charge
Calculate the strength and direction of the electric field
due to a point charge of 2.00 nC (nano-Coulombs) at a distance of 5.00 mm from the charge.
Strategy
We can find the electric field created by a point charge by using the equation
.
Solution
Here
C and
m. Entering those values into the above equation gives
Discussion
This
electric field strength is the same at any point 5.00 mm away from the charge
that creates the field. It is positive, meaning that it has a direction pointing away from the charge
.
Calculating the force exerted on a point charge by an electric field
What force does the electric field found in the previous example exert on a point charge of
?
Strategy
Since we know the electric field strength and the charge in the field, the force on that charge can be calculated using the definition of electric field
rearranged to
.
Solution
The magnitude of the force on a charge
exerted by a field of strength
N/C is thus,
Because
is negative, the force is directed opposite to the direction of the field.
Discussion
The force is attractive, as expected for unlike charges. (The field was created by a positive charge and here acts on a negative charge.) The charges in this example are typical of common static electricity, and the modest attractive force obtained is similar to forces experienced in static cling and similar situations.
Play ball! Add charges to the Field of Dreams and see how they react to the electric field. Turn on a background electric field and adjust the direction and magnitude.
Section summary
The electrostatic force field surrounding a charged object extends out into space in all directions.
The electrostatic force exerted by a point charge on a test charge at a distance
depends on the charge of both charges, as well as the distance between the two.
The electric field
is defined to be
where
is the Coulomb or electrostatic force exerted on a small positive test charge
.
has units of N/C.
The magnitude of the electric field
created by a point charge
is
where
is the distance from
. The electric field
is a vector and fields due to multiple charges add like vectors.
Conceptual questions
Why must the test charge
in the definition of the electric field be vanishingly small?
Calculate the initial (from rest) acceleration of a proton in a
electric field (such as created by a research Van de Graaff). Explicitly show how you follow the steps in the Problem-Solving Strategy for electrostatics.
(a) Find the direction and magnitude of an electric field that exerts a
westward force on an electron. (b) What magnitude and direction force does this field exert on a proton?
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