Electric interactions in electrostatics is the study of forces between numerous charges. When there are several point charges present, each one applies an electric force to the others, and the sum of the effects of all these separate forces determines the total force acting on any given charge.
Coulomb’s Law
We should review Coulomb’s Law. According to Coulomb’s Law, the electrostatic force F between two point charges, q1 and q2, spaced apart by r, is determined by:
F = ke ∣q1q2∣ / r2
Where ke is the Coulomb constant, approximately equal to 9 × 109 Nm2 C−2
Force Between Multiple Charges
When two charges are of opposing signs, the force acting along the line connecting them is attracting; when the charges are like, it is repulsive.
Principle of Superposition
The net force is determined using the superposition principle when there are more than two charges present. This concept states that the vector sum of the forces applied by each of the other charges separately is the total force acting on a particular charge.
Suppose we have three charges q1, q2, and q3. The total force F1 on charge q1 is given by:
F1 = F21 + F31
Where:
F21 is the force on q1 due to q2,
F31 is the force on q1 due to q3.
Each force is calculated separately using Coulomb’s Law and then added vectorially.
If more charges are present, this summation extends to include the force from each additional charge:
F1 = Fi1 i ≠ 1
For example, if two forces act at an angle θ to each other, the magnitude of the resultant force F can be found using:
F2 = F12 + F22 + 2F1F2 cosθ
Examples of Force Between Multiple Charges
Linear Arrangement
It is simple to sum forces algebraically when charges are arranged in a straight line, such as on the x-axis, taking into account their directions (positive or negative depending on attraction or repulsion).
For example, the net force on q2 would be the sum of the forces from q1 and q3 if three charges, q1, q2, and q3, were arranged on a line.
Triangular Arrangement
Symmetry can make things easier if charges are positioned at the corners of an equilateral triangle. To determine the final force, the forces can be broken down into their component parts along the x and y axes and then added together.
An equilateral triangle has three equal charges positioned at its vertices. The amount of each force will be the same, but their directions will differ. Simple vector addition can be used to determine the resulting force on each charge because of symmetry.
Important Points to Remember
Forces between charges obey Newton’s third law: if charge q1 exerts a force F on q2, then q2 exerts a force −F on q1.
Only electric forces are considered in this context; gravitational and other forces are neglected unless stated otherwise.
The net force depends on the magnitudes of the charges, their signs, and the geometric arrangement.
Summary
Electrostatic systems requires a grip of the forces that exist between many charges. One may methodically calculate the net force acting on any charge by applying Coulomb’s equation and the superposition principle. Vector addition is a fundamental ability for further research in electrostatics and beyond since it is necessary to solve problems involving many charges.
MCQ Quiz:
1.The force on a charge due to multiple charges is calculated by:
(a) Adding magnitudes of individual forces
(b) Vector sum of individual forces
(c) Subtracting forces
(d) None of the above
Answer: (b) Vector sum of individual forces
2. If two like charges are placed close to each other, they will:
(a) Attract each other
(b) Repel each other
(c) Neither attract nor repel
(d) First attract then repel
Answer: (b) Repel each other
3. In an arrangement of three equal charges placed at the corners of an equilateral triangle, the net force on each charge is:
(a) Zero
(b) Directed towards the center
(c) Along one side of the triangle
(d) Along the perpendicular bisector of one side
Answer: (b) Directed towards the center
4. According to Coulomb’s law, the force between two charges is directly proportional to:
(a) Square of distance
(b) Product of their magnitudes
(c) Sum of their magnitudes
(d) Inverse of their distance
Answer: (b) Product of their magnitudes
5. What happens to the force if the distance between two charges is doubled?
(a) It becomes four times
(b) It becomes half
(c) It becomes one-fourth
(d) It remains the same
Answer: (c) It becomes one-fourth
6. The principle of superposition is applicable to:
(a) Only two charges
(b) Only like charges
(c) Any number of charges
(d) Only opposite charges
Answer: (c) Any number of charges
