Physics

Problem

Two identical positive point charges, each of magnitude

+4.0\,\mu\text{C}

, are fixed on the

x

-axis at

x = -0.15\,\text{m}

and

x = +0.15\,\text{m}

, respectively. A third point charge of magnitude

-6.0\,\mu\text{C}

is fixed on the

y

-axis at

y = +0.20\,\text{m}

. A

+1.0\,\mu\text{C}

test charge is placed at the origin. (a) Calculate the

x

- and

y

-components of the electrostatic force exerted on the test charge by each of the three fixed charges. Show all work symbolically before substituting numerical values. (b) Determine the magnitude and direction of the net force acting on the test charge. Express the direction as an angle measured counter-clockwise from the positive

x

-axis.

Intuitive explanation

This problem tests your understanding of superposition of electric forces — the idea that the net force on a charge is the vector sum of forces from all other charges. The key insight is to recognize the symmetry: the two identical positive charges are equidistant from the origin and positioned symmetrically about the $y$ -axis, so their horizontal force components cancel, leaving only vertical components to add. Calculate each force magnitude using Coulomb's law, resolve forces into components, then add them vectorially to find the net force on the test charge.

Intuitive explanation

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