Electric Fields: AP Physics 2 Exam Question

Question:

Three point charges are arranged as shown below:

Q1 (+4 μC) --------------- Q2 (-2 μC)

             ↑
 **Q3** (-3 μC)

The distance between Q1 and Q2 is 0.5 meters, and the distance between Q1 and Q3 is 0.3 meters. The electric field intensity at a point P, located on a line perpendicular to the line joining Q1 and Q2, is measured as 7.7 × 10^4 N/C.

1. Determine the magnitude and direction of the electric field intensity due to Q1 at P.
2. Determine the magnitude and direction of the electric field intensity due to Q2 at P.
3. Calculate the magnitude and direction of the electric field intensity at P due to Q3.
4. Calculate the resultant electric field intensity at point P due to all three charges.

Assume that the positive direction of the electric field intensity is defined as pointing away from positive charges and towards negative charges.

Answer:

1. To calculate the electric field intensity at point P due to Q1, we can use the formula for the electric field intensity:

   

   where E is the electric field intensity, K is the electrostatic constant (9 × 10^9 Nm²/C²), Q is the charge, and r is the distance from the charge to the point where the electric field is being measured.

   Plugging in the values:

   

2. To calculate the electric field intensity at point P due to Q2, we can use the same formula as above, but change the sign of the charge Q since it is negative:

   

3. To calculate the electric field intensity at point P due to Q3, we can again use the same formula:

   

4. To find the resultant electric field intensity at point P due to all three charges, we can simply add the electric field intensities:

   

   where to 3, representing Q1, Q2, and Q3.

   The magnitude and direction of the resultant electric field intensity can be found by using the Pythagorean theorem and the inverse tangent:

   

   

   Note: The direction indicates the angle with respect to the positive x-axis in counterclockwise direction.

Note: Evaluating the given equations would provide the specific values based on the question details and calculations would give the final answer.