Point charge q1=-5.00 nC is on the x -axis at x=-0.400 m. Point P is on the x -axis at x=+0.200

step 1 Here for the solution, this is the charge Q1, charge Q2, E1, point P, and E2, the X is equal to

Point charge q1=-5.00 nC is on the x -axis at x=-0.400 m....

Point charge $q_{1}=-5.00 \mathrm{nC}$ is on the $x$ -axis at $x=-0.400 \mathrm{~m}$. Point $P$ is on the $x$ -axis at $x=+0.200 \mathrm{~m}$. Point charge $q_{2}$ is at the origin. What are the sign and magnitude of $q_{2}$ if the resultant electric field at point $P$ is zero?

Key Concepts

Vector Addition in Electrostatics

Since electric fields are vector quantities, their addition must consider both magnitude and direction. The net electric field is obtained by adding the field vectors produced by each charge, which involves analyzing how the fields interact based on the positions and signs of the charges.

Coulomb's Law

Coulomb's Law describes the strength and direction of the electric force between two point charges. It states that the magnitude of the electric field due to a point charge decreases with the square of the distance from the charge. This law is fundamental in calculating the contribution of each charge to the electric field at a given point.

Electric Field Superposition Principle

The superposition principle indicates that the total electric field at any point due to several charges is the vector sum of the electric fields produced by each individual charge. This concept allows one to separately calculate each charge's influence and then combine them to find the overall effect.

Inverse Square Law Dependence

The electric field strength produced by a point charge follows an inverse square law with respect to distance. This means that the effect of a charge on a point in space diminishes as the distance from the charge increases, and this distance dependence is crucial when balancing fields from different charges.

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