A point particle with charge q=4.5 μC is placed on the x...

A point particle with charge $q=4.5 \mu \mathrm{C}$ is placed on the $x$ axis at $x=-10 \mathrm{cm} .$ A second particle of charge $Q$ is now placed on the $x$ axis at $x=+25 \mathrm{cm},$ and it is found that the electric field at the origin is zero. Find $Q$.

Key Concepts

Superposition Principle in Electrostatics

The superposition principle states that when multiple charges are present, the total electric field at any point in space is the vector sum of the electric fields produced by each charge individually. This principle allows for complex configurations of charges to be analyzed by breaking the problem down into simpler parts where the fields of single charges are calculated and then summed.

Charge Sign and Field Direction

The sign of a charge is critical in determining the direction of the electric field it produces. A positive charge generates a radially outward field, while a negative charge generates a radially inward field. This concept is essential when balancing contributions from multiple charges, as the direction of each field vector plays a key role in whether they cancel or reinforce each other.

Electric Field of a Point Charge

The electric field created by a point charge is defined as the force per unit charge experienced by a small positive test charge placed in the field. It is given by Coulomb’s constant multiplied by the source charge divided by the square of the distance from the source charge, and its direction is determined by the sign of the charge: pointing away from a positive charge and toward a negative charge.

Coulomb's Law

Coulomb’s Law describes the force between two point charges, stating that the force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance that separates them. It is a fundamental principle in electrostatics, setting the groundwork for understanding how charges interact through the electric force.

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