Three point charges are located at the corners of an equilateral triangle, as shown below. 

Let

q1 = +18.0 x 10-6C
q2 = +63.0 x 10-6C
q3 = -36.0 x 10-6C
a = 50.0 cm

Find the magnitude and direction of the electrostatic force acting on charge q1 due to the other two charges.

Problem Solving Strategy

Charge q1 experiences an electrostatic force from both of the other charges. To get the total force, you simply add the two constituent forces together. However, since force is a vector quantity, you must add the constituent forces together as vectors rather than scalars (ordinary numbers). Each vector constituent has a magnitude given by Coulomb’s Law and direction given the properties of electrostatic force.

Here are the steps you should follow to solve this problem:

  1. Draw a vector diagram using the basic properties of electrostatic forces between point charges.
  2. Find the magnitudes of each constituent force using Coulomb’s Law.
  3. Use your vector diagram to sum the components of the constituent forces to calculate each component of the resultant force.
  4. Use these components to calculate the magnitude and direction of the resultant.
  5. Complete the vector diagram started in part 1 above by adding the resultant vector to the sketch.

Although it is sometimes possible to shorten the solution substantially using symmetry, the above procedure will always work to solve this type of problem.

Step One: The Vector Diagram

Each charge experiences a force due to the other two charges, and solving this problem simply involves adding these two forces together. Since force is a vector quantity, it is very important that you begin your solution with a vector diagram.

You should make a sketch of the correct vector diagram for this problem for later use.

The vector diagram that characterizes the electrostatic forces on charge q1 due to both q2 and q3 is
a
b
c
d
None of the above.

Step Two: Find the Magnitudes

The next step is to find the magnitudes of each of the two constituent forces.

The electrostatic force on charge q1 due to q2 has magnitude N

The electrostatic force on charge q1 due to q3 has magnitude N

Step Three: Sum the Components

Use the vector diagram that you sketched in part a to determine the x and y components of the resultant force.

The x component of the resultant electrostatic force on charge q1 is N

The y component of the resultant electrostatic force on charge q1 is N

Step Four: Magnitude and Direction of the Resultant

Sketch the resultant force on your vector diagram and calculate the magnitude of the vector and the angle it makes with one of your axes.

We might as well use the positive x axis to calculate the angle.

The magnitude of the resultant electrostatic force on charge q1 is N

The angle that the resultant makes with the positive x axis is
4.7 degrees
-85.3 degrees
265.3 degrees
184.7 degrees
1.488 degrees


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