Question
Three point charges of μC, μC, and μC are placed at the vertices of an equilateral triangle of side m. Find the magnitude of the net electrostatic force on the μC charge. Take N·m/C.
Solution — Step by Step
The two μC charges each attract the μC. Each pair force:
So each μC pulls the μC with N along the line joining them.
The two μC charges sit at vertices of an equilateral triangle, with the μC at the third vertex. The two attractive force vectors on the μC point from its position toward each of the other two vertices. The angle between these vectors equals the interior angle of the triangle at the μC vertex, which is .
Final Answer: N (directed along the perpendicular bisector toward the μC pair).
Why This Works
Coulomb’s law gives the magnitude of force between two charges; for multiple charges, we use vector superposition. In an equilateral arrangement, the symmetry makes the angle between any two pair-forces equal to , which simplifies the parallelogram-law calculation to .
The direction of the net force is along the symmetry axis (the perpendicular bisector of the line joining the two like charges), pointing toward them since the test charge is being attracted.
Alternative Method
Resolve each force into x- and y-components along this symmetry axis. The components perpendicular to the axis cancel, and the components along the axis add: . Same answer, different route.
Adding the magnitudes directly ( N) ignores that forces are vectors. This works only if both forces are parallel — never assume that without checking the geometry.
This exact configuration (with sign flips) appears in JEE Main almost every year. The trick to fast solving: spot the symmetry first, then compute one pair-force, then multiply by the right geometric factor ( for , for ).