A charge Q0 is at the origin. A second charge, Qx=2 Q0, is...

A charge $Q_{0}$ is at the origin. A second charge, $Q_{x}=2 Q_{0},$ is brought from infinity to the point $x=a, y=0 .$ Then a third charge $Q_{y}$ is brought from infinity to $x=0, y=a$. If it takes twice as much work to bring in $Q_{y}$ as it did $Q_{x}$, what's $Q_{y}$ in terms of $Q_{0} ?$

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Key Concepts

Electric Potential

Electric potential is a measure of the potential energy per unit charge at a point in a field created by other charges. It depends on both the magnitude of the source charge and the distance from it, as described by Coulomb's law, and it follows the principle of superposition, meaning that the net potential due to several charges is the sum of the potentials due to each individual charge.

Work in an Electrostatic Field

In electrostatics, the work required to bring a charge from infinity to a certain point in an electric field is determined by the electric potential at that point. This work is given by the product of the charge being moved and the electric potential created by the other charges. This concept is key to understanding energy changes in systems of point charges.

Superposition Principle in Electrostatics

The superposition principle states that the total electric potential at a given point is the algebraic sum of the potentials due to each individual charge present. This principle allows complex problems involving multiple charges to be broken down into simpler ones, where the contributions from individual charges can be calculated and then summed to find the overall potential.

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