Q2. Three positive particles of equal charge are located at the corners of an equilateral triangle of side 15.0 cm. Calculate the magnitude and direction of the net force on each particle due to the other two.

Background

Topic: Electrostatics – Coulomb's Law and Vector Addition

This question tests your understanding of how to calculate the net electrostatic force on a charge due to other point charges, using Coulomb's law and vector addition. The symmetry of the equilateral triangle is key to solving the problem.

Key Terms and Formulas

• Coulomb's Law:

• = Coulomb's constant

• = charges (in Coulombs)

• = distance between charges (in meters)

• Vector addition: Forces are vectors and must be added using components.

Step-by-Step Guidance

1. Convert all quantities to SI units: , .

2. Calculate the magnitude of the force between any two charges using Coulomb's law:

3. Draw a diagram showing the forces acting on one charge due to the other two. Each force will be directed away from the charge (since all are positive and repel each other).

4. Resolve the two force vectors into their x and y components. Use the geometry of the equilateral triangle to determine the angles (each angle is 60°).

5. Add the components to find the net force vector on one charge. Set up the expressions for the net x and y components, but do not compute the final values yet.

Try solving on your own before revealing the answer!

Q5. Use Coulomb's law to determine the magnitude and direction of the electric field at points A and B in the figure below due to the two positive charges () shown. Draw the electric field vectors for each charge and the net electric field at both points.

Background

Topic: Electric Fields from Point Charges (Coulomb's Law)

This question tests your ability to calculate the electric field at specific points due to multiple point charges, and to use vector addition to find the net field.

Key Terms and Formulas

• Electric Field from a Point Charge:

• Direction: Away from positive charges, toward negative charges.

• Superposition Principle: The net electric field is the vector sum of the fields from each charge.

Step-by-Step Guidance

1. Convert all quantities to SI units: , distances in meters.

2. For each point (A and B), calculate the distance from each charge to the point using the Pythagorean theorem if needed.

3. Calculate the electric field magnitude from each charge at the point using .

4. Draw the direction of each electric field vector at the point (away from each charge, since they are positive).

5. Resolve the electric field vectors into x and y components, and set up the expressions for the net electric field at each point. Do not compute the final values yet.

Try solving on your own before revealing the answer!