22.6:
Coulomb’s Law and The Principle of Superposition
Coulomb's law describes the force between two point charges, q-1 and q-2. What is the force experienced by a third point charge, Q?
q-1 and q-2 are called source charges, and Q is called the test charge. Let Q experience force F-1 due to q-1, and F-2 due to q-2.
Experiments show that the net force experienced by the test charge is the vector sum of F-1 and F-2. This is called the principle of superposition.
If there are more than two source charges, the force on the test charge can be calculated similarly.
Imagine the test charge is an electron at the origin; q-1 equals +8-e, placed on the x-axis at a distance 2-d from the origin, and q-2 equals +18-e, placed on the y-axis at 3-d from the origin. Then, F-1 and F-2 turn out to be equal in magnitude, directed along the x and y axes, respectively.
Hence, the net force on Q is about 1.4 times this magnitude and is directed at 45 degrees to the x-axis.
22.6:
Coulomb’s Law and The Principle of Superposition
Coulomb's Law describes the force experienced by two point charges under each other's presence. But what if there are more than two charges? For example, if there is a third charge, does it experience a force that is a simple combination of the individual forces due to the first two charges? Can it be described mathematically?
The Principle of Superposition answers the question. Yes, Coulomb's Law applies to each pair of charges, and the net force on each charge is the vector sum of the individual forces on it due to all the other charges. Hence, the principle of superposition formulates a single vector describing the force experienced by a test charge.
Note that the force need not have been such a simple function of the two forces but could be a more complicated function. Thankfully, nature follows this simple principle.
However, note that the principle also applies to all the other charges. Hence, each pair of forces causes the others to accelerate. Thus, unless they are held together in their positions by external forces, each starts moving, thereby changing the individual forces, that changes the net force on each charge, which in turn changes its acceleration. As a result, the mathematical problem is a difficult one.
Suggested Reading
- OpenStax. (2019). University Physics Vol. 2. [Web version]. Retrieved from https://openstax.org/details/books/university-physics-volume-2; section 5.3; page 195.