Coulomb's law Flashcards
Coulomb’s law
Coulomb’s law states that any two point charges exert an electrical force on each other that is proportional to the product of their charges and inversely proportional to the square of the distance between them.
Coulomb’s law formula
F = Q1Q2 / 4π ε0 r^2
(ε0 = 8.85 x 10^−12)
One of the direct consequence of Coulomb’s law
Doubling the separation results in one-quarter of the force.
What do the forces between two charges with positive and negative signs indicate?
If we have a positive and a negative charge, then the force F is negative. We interpret this as an attraction. Positive forces, as between two like charges, are repulsive. In gravity, we only have attraction.
Formula for Electric field strength due to a point charge Q
E = Q / 4π ε0 r^2
How to derive Electric field strength for a point charge?
(Definition : The electric field strength is the force at a point per unit positive charge at the point)
To find the field strength near a point charge Q1 (or outside a uniformly charged sphere), we have to imagine a small positive test charge Q2 placed in the field, and determine the force per unit charge on it. We can then use the definition to determine the electric field strength for a point (or spherical) charge. The force between the two point charges is given by:
F = Q1Q2 / 4π ε0 r^2
The electric field strength E due to the charge Q1 at a distance of r from its centre is thus:
E = force / test charge
E = Q1Q2 / 4π ε0 r^2 Q2
E = Q / 4π ε0 r^2
Relationship between Electric field strength and distance
The field strength E is not a constant; it decreases as the distance r increases. The field strength obeys an inverse square law with distance–just like the gravitational field strength for a point mass. The field strength will decrease by a factor of four when the distance from the centre is doubled.
Note also that, since force is a vector quantity, it follows that electric field strength is also a vector. We need to give its direction as well as its magnitude in order to specify it completely (for a point charge). If it’s required to find E due to two point charges; then calculate E for both and find resultant.
Formula for work done or change in potential energy in moving a point charge (from i.e. a negative plate to a positive plate)
W = VQ
Potential difference formula and definition
Potential difference is defined as the energy change (joules) per unit charge (coulombs) between two points. Hence, for charge Q, the work done in moving it from the negative plate to the positive plate is: W = VQ
We can rearrange this equation as:
V = W / Q
This is really how voltage V is defined. It is the energy per unit positive charge at a point in an electric field. By analogy with gravitational potential, we call this the electric potential at a point. Now you should be able to see that what we regard as the familiar idea of voltage should more correctly be referred to as electric potential. The difference in potential between two points is the potential difference (p.d.) between them.
Electric potential definition
The electric potential at a point is equal to the work done per unit charge in bringing unit positive charge from infinity to that point.
Formula for Electric potential (in a radial field due to a point charge)
V = Q / 4π ε0 r
(This comes from the calculus process of integration, applied to the Coulomb’s law equation.)
Note that we do not need the minus sign in the electric equation as it is included in the charge. A negative charge gives an attractive (negative) field whereas a positive charge gives a repulsive (positive) field.
Defining zero of potential
A charge has zero potential energy when it is at infinity (some place where it is beyond the influence of any other charges). If we move towards a positive charge, the potential is positive. If we move towards a negative charge, the potential is negative. This allows us to give a definition of electric potential: The electric potential at a point is equal to the work done per unit charge in bringing unit positive charge from infinity to that point. Electric potential is a scalar quantity. To calculate the potential at a point caused by more than one charge, find each potential separately and add them. Remember that positive charges cause positive potentials and negative charges cause negative potentials.
Potential energy overview
For instance, we can think about moving a positive charge in a uniform electric field between two charged parallel plates. If we move the charge towards the positive plate, we have to do work. The potential energy of the charge is therefore increasing. If we move it towards the negative plate, its potential energy is decreasing.
Formula for Electrical potential energy of a pair of point charges (+ derivation)
Electric potential energy between two points A and B as the work done in moving positive charge from point A to point B. This means that the potential energy change in moving point charge Q1 from infinity towards a point charge Q2 is equal to the potential at that point due to Q2 multiplied by Q1. In symbol form:
W = V x Q2
The potential V near the charge Q2 is:
V = Q2 / 4π ε0 r
Thus the potential energy of the pair of point charges W (shown as Ep in the equation) is:
Ep = Qq / 4π ε0 r
Formula for Potential difference between two points from a charge
The potential difference between two points, one at a distance r1 and the second at a distance r2 from a charge Q is:
ΔV = Q /4π ε0 [1 / r1 − 1 / r2]
