What is the expression for force in a current carrying conductor?

Question

Examoogle · Accepted Answer

Option C: $F = \frac{K q_1 q_2}{r^2}$

Explanation & Concepts:
The force of interaction between two point charges is governed by Coulomb's Law, which states that the force is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. Although the question title references a 'current carrying conductor', the provided options define the electrostatic force between two point charges.

Working Principle: The principle relies on the inverse-square law for electric fields created by stationary charges. When two point charges $q_1$ and $q_2$ are placed at a distance $r$ in a medium, the electrostatic force $F$ acts along the line joining them, with $K$ being the Coulomb's constant.

Key Formulas: $F = \frac{K q_1 q_2}{r^2}$ — Coulomb's Law for electrostatic force; $K = \frac{1}{4 \pi \epsilon_0}$ — Coulomb's constant in vacuum

Key Points: Electrostatic force is a vector quantity.; The force is attractive for unlike charges and repulsive for like charges.; Coulomb's law is valid for point charges at rest.

Advantages: Provides a simple mathematical model for point interactions.; Fundamental basis for understanding electric fields.

Disadvantages: Does not account for relativistic effects at high speeds.

Applications: Calculation of field intensities.; Design of electrostatic sensors and MEMS devices.

Additional Info: Note: The question text mentions a 'current carrying conductor' but the options provided are strictly for electrostatic force. If the question intended magnetic force on a conductor, the formula would involve $F = I(L 	imes B)$.. Options A, B, and D are dimensionally incorrect for the electrostatic force law.

Answer: C is correct — The electrostatic force between two point charges is given by Coulomb's Law, defined as $F = \frac{K q_1 q_2}{r^2}$.

Exam Tip: Always verify if the question asks for electrostatic force (Coulomb's Law) or electromagnetic force (Lorentz Force) before applying the formula.

Examoogle · Answer

Option A: $F = \frac{K}{r^2}$

Examoogle · Answer

Option B: $F = \frac{Kq}{r^2}$

Examoogle · Answer

Option D: $F = \frac{K q_1 q_2}{r}$

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