Pregunta
20.2 Calculate the net electrostatio force that
and
exert on
.
Ask by Page Cummings. in South Africa
Mar 14,2025
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The net electrostatic force on
is
downward.
Solución
We will illustrate a complete solution by assuming the following configuration. (In your particular textbook the numbers and positions may differ. In our example the values below are assumed.)
Assume that three point charges are located at the vertices of an isosceles “horizontal‐base” triangle as follows:
• Charge
is at point
.
• Charge
is at point
.
• Charge
is at point
.
When a negative charge is attracted toward a positive charge the force on the negative charge points toward the positive charge. Thus the force on
due to
(denoted
) points from
toward
, and the force on
due to
(denoted
) points from
toward
.
Below are the step‐by‐step calculations.
1. Determine the Distances
The distance from
to either
or
is given by the distance formula. For example, for
to
:
Similarly,
2. Compute the Magnitudes of the Forces
Coulomb’s law gives the magnitude of the force between two point charges:
where
. First, express all charges in Coulombs:
Since the distance squared is
the magnitude of the force exerted by
on
is
Calculate the product in the numerator:
Thus,
Multiply the numbers:
so
Because of symmetry, the force from
on
has the same magnitude:
3. Determine the Directions and Components of the Forces
Force
:
The force on due to
points from
at
toward
at
. The vector from
to
is
The force on
Its magnitude is
Thus the unit vector in the direction from
to
is
So, the vector force is
Force
:
The force on due to
points from
at
toward
at
. The vector from
to
is
The force on
Its magnitude is also
Thus the unit vector is
Then,
4. Find the Net Force on
The net force on
is the vector sum
Adding the components:
-
-component: -
-component:
Thus,
[
\vec{F}_{net} = \left(0
\vec{F}_{net} = \left(0
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Extra Insights
To calculate the net electrostatic force that charges
and
exert on charge
, you first need to determine the individual forces using Coulomb’s Law, which states that the force
between two point charges is given by:
where
is Coulomb’s constant (
),
and
are the magnitudes of the charges, and
is the distance between them. Once you find
(the force exerted by
on
) and
(the force exerted by
on
), you can determine the direction of these forces based on the signs of the charges. The net force is found by vectorially adding
and
.
From here, remember that forces acting in the same direction will add together, while forces acting in opposite directions will subtract.
Lastly, make sure to double-check your distances and charge values, as miscalculations can significantly alter your results. Keeping track of the signs for attraction and repulsion based on charge polarity is essential for accurate computations!

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