Three point charges are placed on the x -axis. A charge of 3.00 μC is at the origin. A charge of

step 1 Let me draw a figure for the given problem. This is our y -axis, right? And this one is x -axis.

Three point charges are placed on the x -axis. A charge of...

Three point charges are placed on the $x$ -axis. A charge of $3.00 \mu \mathrm{C}$ is at the origin. A charge of $-5.00 \mu \mathrm{C}$ is at $20.0 \mathrm{cm},$ and a charge of $8.00 \mu \mathrm{C}$ is at $35.0 \mathrm{cm} .$ What is the force on the charge at the origin?

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Key Concepts

Charge Sign and Force Direction

The sign of a charge determines whether the force between two charges will be attractive or repulsive. Like charges repel each other, while opposite charges attract. This concept is crucial for determining the direction of the forces acting on a charge when multiple other charges are present.

Vector Addition of Forces

Since electric forces are vector quantities, they must be added using vector addition. This involves considering both the magnitude and direction of each individual force, ensuring that contributions along each axis are summed correctly to determine the net force on the charge.

Superposition Principle

The superposition principle states that when multiple forces act on a single charge, the total force is the vector sum of all individual forces. This means that forces from each charge can be calculated independently and then combined, taking into account both magnitude and direction.

Coulomb's Law

Coulomb's Law defines the electric force between two point charges. It states that the magnitude of the force is proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. The law also indicates that the force is attractive if the charges have opposite signs and repulsive if the charges have the same sign.

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