Three point charges are fixed at the vertices of an equilateral triangle of side 0.10 m
PHYSICS · Multi-part · A Level · Physics · Fields and their consequences · Fields and their consequences
Problem
Three point charges are fixed at the vertices of an equilateral triangle of side 0.10 m. Charges q₁ = +4.0 μC and q₂ = +4.0 μC occupy the two lower vertices located at (0, 0) m and (0.10 m, 0), respectively. Charge q₃ = −6.0 μC is located at the upper vertex at (0.050 m, 0.0866 m).
(a) Calculate the electric force exerted on q₃ by q₁ and, separately, the electric force exerted on q₃ by q₂. Express each force in component form (Fx, Fy) with appropriate units.
(b) Determine the magnitude and direction (angle measured counter-clockwise from the +x-axis) of the net electric force on q₃ caused by q₁ and q₂ together.
(c) A fourth point charge q₄ is to be placed at the centroid of the triangle, whose coordinates are (0.050 m, 0.0289 m). Find the magnitude and sign of q₄ that will make the net electric force on q₃ exactly zero once q₄ is in place. Show all reasoning and calculations.