Two point charges +8 q and -2 q are located at x=0 and x=L,...

Two point charges $+8 q$ and $-2 q$ are located at $x=0$ and $x=L$, respectively. The location of a point on the $x$-axis at which the net electric field due to these two point charges is zero
(A) $2 L$
(B) $\frac{L}{4}$
(C) $8 L$
(D) $4 L$

Key Concepts

Equilibrium Points in Electric Fields

Equilibrium points are locations where the net electric field is zero due to the cancellation of contributions from multiple charges. Identifying such points involves setting the algebraic sum of the individual electric fields to zero and solving for the positions where this condition holds. This concept is crucial for understanding the balance of forces in systems with multiple charges.

Coulomb's Law

Coulomb's Law is fundamental for calculating the electric force between two point charges. It 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. This law provides the basis for determining the strength of the electric field generated by a point charge at a specific location in space.

Electric Field Due to a Point Charge

The electric field due to a point charge is a vector field that represents the force per unit charge exerted on a test charge placed in its vicinity. The magnitude of this field decreases with the square of the distance from the charge, and its direction depends on the sign of the charge—emanating outward for positive charges and directed inward for negative charges.

Superposition Principle

The superposition principle states that the net electric field created by multiple charges is the vector sum of the electric fields produced by each individual charge. This principle allows for the calculation of complex electric fields by analyzing the contributions from each point charge separately and then combining them to find the overall field at a particular point in space.

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