Principle of Superposition
States that the total electrostatic force on a given charge due to a number of other charges is the vector sum of the individual forces exerted on that charge by all other charges.
What is Principle of Superposition?
The force of attraction or repulsion between two electrically charged particles.
Key formula / rule: Vector Sum of Forces
Key points
- Understand that electrostatic forces are additive.
- Be able to calculate the net force on a charge in a system of multiple charges.
- Apply vector addition to find the resultant force.
Common exam trap
Treating the forces as scalar sums instead of vector sums.
Definitions
- Term
Electrostatic Force
- Meaning
The force of attraction or repulsion between two electrically charged particles.
- Term
Vector Sum
- Meaning
The sum of two or more vectors, taking into account their magnitudes and directions.
Learning objectives
Understand that electrostatic forces are additive.
Be able to calculate the net force on a charge in a system of multiple charges.
Apply vector addition to find the resultant force.
Formulae
- Name
Vector Sum of Forces
- Note
Where Fi is the electrostatic force on the charge due to the i-th other charge.
- Expression
Fnet = F1 + F2 + F3 + ... + Fn
- Name
Coulomb's Law (for individual force)
- Note
This formula calculates the magnitude and direction of the force between two point charges qi and qj separated by distance rij.
- Expression
Fij = \frac{1}{4\π\ε0} \frac{|qi qj|}{rij^2} \hat{r}_{ij}
Prerequisites
Coulomb's Law
Vector addition
Concept of point charges
Common mistakes
Treating the forces as scalar sums instead of vector sums.
Ignoring the direction of individual forces.
Incorrectly calculating the magnitude or direction of individual Coulomb forces.
Assuming the principle applies to non-electrostatic forces.
Keywords
Superposition Principle
Electrostatics
Vector Sum
Coulomb's Law
Multiple Charges
Net Force
Practice preview
Two point charges +Q are placed at (0, a) and (0, -a) on the y-axis. A third point charge -Q is placed at (x, 0) on the x-axis. What is the magnitude of the net electrostatic force on the charge -Q?…
hard
Three charges +q, +q, and -q are placed at the vertices of an equilateral triangle of side 'a'. What is the magnitude of the net electrostatic force on the charge -q?…
medium
Four point charges, each of magnitude +Q, are placed at the four corners of a square of side 'a'. What is the net electrostatic force on a charge +q placed at the center of the square?…
medium