Questions: Three point charges have equal magnitudes and are fixed to the corners of an equilateral triangle. Two of the charges are positive and one is negative, as the drawing shows. At which one of the corners is the net force acting on the charge directed parallel to the x axis? B A C

Solution Steps

• The charges are located at the corners of an equilateral triangle.
• Let's denote the charges at points A, B, and C.
• Two charges are positive, and one charge is negative.

• The force between two charges is given by Coulomb's law: \( F = k \frac{|q_1 q_2|}{r^2} \).
• Since the triangle is equilateral, the distance between any two charges is the same.

• For charge at A (positive):
  • It experiences repulsive forces from charges at B and C.
  • The forces from B and C will have components in both x and y directions.
• For charge at B (positive):
  • It experiences repulsive force from charge at A and attractive force from charge at C.
  • The forces will have components in both x and y directions.
• For charge at C (negative):
  • It experiences attractive forces from charges at A and B.
  • The forces will have components in both x and y directions.

• For charge at A:
  • The x-components of the forces from B and C will cancel each other out due to symmetry.
  • The y-components will add up, resulting in a net force in the y direction.
• For charge at B:
  • The x-components of the forces from A and C will not cancel out.
  • The y-components will cancel each other out due to symmetry.
• For charge at C:
  • The x-components of the forces from A and B will cancel each other out due to symmetry.
  • The y-components will add up, resulting in a net force in the y direction.

Final Answer