Four point charges are located at the corners of a square, as shown.
Let

q1 = +18 x 10-9C
q2 = q3 = q4 = -18 x 10-9C
a = 50 cm

  1. Find the magnitude and direction of the electric field at the position of q3 due to the other three charges.
  2. Use the result of part a to find the magnitude and direction of the electrostatic force on charge q3.

Part a:

Find the magnitude and direction of the electric field at the position of q3 due to the other three charges.

Step One: The Vector Diagram

Each charge of the three charges q1, q2, and q4 produce an independent electric field at the location of q3. Since each electric field contribution is a vector quantity, you simply have to add three vectors together to work this problem. As in any vector problem, it is important to begin your solution with a vector diagram.

You should make a sketch of the correct vector diagram for this problem in your solution notes.

The vector diagram that characterizes the electric field at the position of q3 due to charges q1, q2 and q4 is:
a
b
c
d
none of the diagrams are correct
all of the diagrams are correct

Step Two: Find the Magnitudes

The next step is to find the magnitudes of each of the three constituent fields. Complete this step, and record the values in your solution notes.

As a check, you should find that the electric field at the position of charge q3 due to q1 has magnitude 323.55N/C

Step Three: Sum the Components

Use the vector diagram that you sketched in part a and the results of step two to determine the x and y components of the resultant field.

The x component of the resultant electric field at the position of charge q3 is N/C

The y component of the resultant electric field at the position of charge q3 is N/C

Step Four: Magnitude and Direction of the Resultant

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

The magnitude of the resultant electric field at the posistion of charge q3 is N/C

The angle the resultant makes with the positive x-axis is
45 degrees
-45 degrees
135 degrees
225 degrees
315 degrees
None of the above

Step Five: Sketch the Resultant Field on Your Vector Diagram

Your sketch should now look like:

To summarize, here are the steps that you followed to solve Part a of this problem:

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

Now you are ready to work Part b of the problem.

Part b:

Use the result of part a to find the magnitude and direction of the electrostatic force on charge q3.

The magnitude of the electrostatic force on charge q3 due to the other three charges is N

The angle that the electrostatic force on charge q3 makes with the positive x-axis is degrees


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