How to calculate the magnitude of the force between two charges?
We can find the force between any two charges by Coulomb’s law. Coulomb’s law states that two charged bodies will attract or repel each other with a force that is proportional to the product of their charges and inversely proportional to the square of the distance between them,
Let’s get an equation out of this,
Where F is the force of attraction or repulsion depending upon the charges,
k is the coulomb’s constant, for air, it is 9×109 N m2 C-2. Q1 and Q2 are the magnitudes of two charges
d is the distance between the two charges,
This is only applicable for two charged particles, how will we find a force on one charge due to multiple charges?
Let’s consider three charges Q1, Q2, and Q3.
Calculating the total force on a charge entails summing up the vector forces exerted by all other charges, which is known as the superposition theorem.
Let's illustrate this concept using an example involving three point charges: Qa, Qb, and Qc, positioned with vectors r1, r2, and r3, respectively. The force experienced by one charge due to the presence of the other charges can be expressed as:
By applying this to our current situation of 3 point charges we will get,
This is a combination of the coulombs law and the superposition theorem, and any electro static force can be derived using coulombs law and the superposition theorem this way.
- The force acting on a charge is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance between them.
- The force acting on a point charge due to multiple charges is given by the vector sum of all individual forces acting on the charges.
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Jan 06, 2025
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