Two point charges q1 and q2 are 3.00 m apart, and their total charge is 20μC . (a) If the force

step 1 So we are given the data that Q1 plus Q2 is equal to 20 micropoleum. So let's write that down. F

Two point charges q1 and q2 are 3.00 m apart, and their...

Two point charges $q_{1}$ and $q_{2}$ are 3.00 $\mathrm{m}$ apart, and their total charge is 20$\mu \mathrm{C}$ . (a) If the force of repulsion between them is $0.075 N,$ what are magnitudes of the two charges? (b) If one charge attracts the other with a force of $0.525 \mathrm{N},$ what are the magnitudes of the two charges? Note that you may need to solve a quadratic equation to reach your answer.

Two point charges $q_{1}$ and $q_{2}$ are 3.00 $\mathrm{m}$ apart, and their total charge is 20$\mu \mathrm{C}$ . (a) If the force of repulsion between them is $0.075 N,$ what are magnitudes of the two
charges? (b) If one charge attracts the other with a force of $0.525 \mathrm{N},$ what are the magnitudes of the two charges? Note that you may need to solve a quadratic equation to reach your
answer.

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Key Concepts

Quadratic Equations in Physics

When the relationships between charges are expressed through their sum and product, a quadratic equation may naturally arise. Solving this equation provides the individual values of the unknown charges, making quadratic equations a vital tool in analyzing and solving certain electrostatics problems.

System of Equations in Electrostatics

Problems involving point charges often lead to a system of equations where one equation comes from Coulomb's Law (relating charge product to the force) and another from the conservation of charge or a given total charge. Solving these equations simultaneously allows for the determination of individual charge magnitudes.

Coulomb's Law

Coulomb's law states that the electrostatic force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. This law is fundamental in determining the force interactions in problems involving electric charges.

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