Example Question #1 : Electricity And Magnetism
Charges A and B are placed a distance of from one another. The charge of particle A is whereas the charge of particle B is . Charge B experiences an electrostatic force of from charge A. Similarly, charge A experiences an electrostatic force of from charge B.
What is the ratio of to ?
This question is very simple if you realize that the force experienced by both charges is equal.
The definition of the two electrostatic forces are given by Coulomb's law:
In this question, we can rewrite this equation in terms of our given system.
It doesn’t matter if the charges of the two particles are different; both particles experience the same force because the charges of both particles are accounted for in the electrostatic force equation (Coulomb's law). This conclusion can also be made by considering Newton's third law: the force of the first particle on the second will be equal and opposite the force of the second particle on the first.
Since the forces are equal, their ratio will be .
Example Question #1 : Using Coulomb's Law
An excess charge of is put on an ideal neutral conducting sphere with radius . What is the Coulomb force this excess charge exerts on a point charge of that is from the surface of the sphere?
Two principal realizations help with solving this problem, both derived from Gauss’ law for electricity:
1) The excess charge on an ideal conducting sphere is uniformly distributed over its surface
2) A uniform shell of charge acts, in terms of electric force, as if all the charge were contained in a point charge at the sphere’s center
With these realizations, an application of Coulomb’s law answers the question. If is the point charge outside the sphere, then the force on is:
In this equation, is Coulomb’s constant, is the excess charge on the spherical conductor, and is total distance in meters of from the center of the conducting sphere.
Using the given values in this equation, we can calculate the generated force: