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 examp…
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.
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Q1: What is the principle of superposition in electrostatics?
The principle of superposition states that the net force on a test charge equals the vector sum of individual forces from all source charges. When multiple charges act on a test charge, each pair interaction follows Coulomb's law independently. The resulting net force is simply the vector addition of these individual forces, not a more complicated function.
Q2: How do you calculate the net force on a test charge from multiple source charges?
Calculate the force between the test charge and each source charge individually using Coulomb's law. Then add these forces as vectors, accounting for both magnitude and direction. The vector sum of all individual forces gives the net force on the test charge, regardless of how many source charges are present.
Q3: What is the difference between a source charge and a test charge?
Source charges are the charges creating the electric force, while the test charge is the charge experiencing that force. In a system with multiple charges, any charge can be designated as the test charge to find the net force acting on it from all other source charges. This distinction helps organize calculations using the principle of superposition.
Q4: Why does the principle of superposition apply to systems with more than two charges?
Coulomb's law describes the force between any two point charges. Since this pairwise interaction is linear, the total force on a test charge is simply the vector sum of forces from each source charge acting independently. Nature follows this simple additive principle, making complex multi-charge systems mathematically tractable through superposition.
Q5: What happens to the forces in a multi-charge system if the charges are not held in place?
If charges are free to move, each experiences a net force causing acceleration. As charges move, the individual forces between them change, altering the net force on each charge and their accelerations. This creates a complex, dynamic problem where positions continuously change, making mathematical analysis significantly more difficult than static configurations.
Q6: How do you find the direction of the net force using vector addition?
Add the individual force vectors component-by-component along each axis. The resultant vector's magnitude and direction represent the net force. For example, if two equal-magnitude forces act perpendicular to each other, the net force has magnitude 1.4 times the individual force and points at 45 degrees between them.
Q7: How does the principle of superposition relate to sources and properties of electric charge?
The principle of superposition depends on understanding how individual charges create forces. Understanding sources and properties of electric charge provides the foundation for applying Coulomb's law to each charge pair, which is then combined through superposition to find net forces in multi-charge systems.