The attractive electrostatic force between the point charges +8.44 ×10^-6 C and Q has a magnitud

The attractive electrostatic force between the point charges...

The attractive electrostatic force between the point charges
$+8.44 \times 10^{-6} \mathrm{C}$ and $\mathrm{Q}$ has a magnitude of 0.975 $\mathrm{N}$ when the separation between the charges is 1.31 $\mathrm{m} .$ Find the sign and magnitude
of the charge $\mathrm{Q}$ .

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Key Concepts

Coulomb's Law

Coulomb’s Law is a fundamental principle that describes the force between two point charges. It states that the electrostatic force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them, with a proportionality constant known as Coulomb’s constant. This law is crucial for calculating either the force between known charges or determining an unknown charge when the force is given.

Charge Sign and Polarity

The concept of charge sign and polarity is essential in understanding the direction and nature of the electrostatic force. An attractive force between two charges indicates that the charges have opposite signs. Recognizing this relationship helps in determining the sign of an unknown charge when the direction of the force (attraction or repulsion) is specified.

Solving for an Unknown Charge

Determining an unknown charge involves rearranging the formula provided by Coulomb’s Law to solve for the missing variable. This process entails isolating the unknown charge on one side of the equation, substituting known values such as the magnitude of the force, the known charge, and the separation distance, and then solving algebraically. Proficiency in this technique is crucial for problem-solving in electromagnetism.

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