Electrostatic Concepts and Relationships

Guide 20-1. Electrostatic Concepts and Relationships

It's easy to get overwhelmed with the various concepts and relationships for electrostatics. What is fundamental? What is derived? When can you use what relationships? We provide this table to help answer these questions in an organized way. We also include some more general concepts and relationships that we've used throughout the year.

Be cautious of using relationships not given in the table below. Such relationships are probably derived and not fundamental. You're generally expected to start problem solutions with definitions and fundamental laws and relationships. An example of something not to start with is W_el = qEd. This formula makes an assumption about the direction between the force and displacement. You should instead be able to derive the relationship from the more fundamental relationships: W_i = F_idcosθ and E = -ΔV/Δs.
Row	Item	Description	Condition for validity
1	F_el = k\|q₁\|\|q₂\|/r²	Coulomb's Law gives the electrical force between two point charges separated by distance r.	May be used for point charges but not distributions of charges. For example, don't use Coulomb's Law for a charged plate.
2	E = F_el/q₀	Definition of electric field. The direction of the field is the direction of the electric force on a positive test charge placed in the field.	always valid
3	F_el = qE	Given the electric field, this relationship gives the force on charge q placed in the field.	always valid
4	W_i = F_idcosθ	Definition of work. WorkW_i done by a force F_i on an object is the product of the force and the displacement of the object in the direction of the force.	valid for constant forces where the direction between the force and displacement is also constant
5	W_ext = ΔE_sys	Law of conservation of energy	valid when there is no heat transfer into and out of the system (We're not interested in thermal processes here.)
6	ΔU = -W_c	Definition of potential energy. The change in potential energy is the negative of the work done by a conservative force.	always valid
7	ΔU_el = -W_el	Application of the definition of potential energy to electric force	always valid
8	ΔV = ΔU_el/q₀	Definition of potential difference. It is the change in potential energy per unit charge. A charge q₀ placed in the field undergoes a change in potential energy ΔU_el when passing through a potential difference ΔV. Note that rearranging the formula to ΔU_el = q₀ΔV provides a way to calculate the change in electric potential energy, given the charge and potential difference.	always valid
9	E = -ΔV/Δs	Relationship between electric field and potential difference. If a particle undergoes a displacement Δs in the direction of the electric field E, the difference in potential that the particle experiences is -ΔV.	valid for uniform electric fields

Example Problem

This problem illustrates some of the important concepts and relationships above. Click here to open an animation. Read the description accompanying the applet and then run the animation. Here are some important things to note.

The field and the force are in the same direction. (How could you get the field and force to point in opposite directions?)
The field points in the direction in which the electric potential V is decreasing. This is a matter of definition, and is always true. It's a consequence of the negative sign in the relationship E = -ΔV/Δs and the fact that Δs is defined to be in the direction of E.
The electric potential energy U_el (not the same as electric potential) is greatest when a positive particle is next to the positive plate and when a negative particle is next to the negative plate. U_el decreases as the particle moves away from the plate.
The work done by the electric field W_el increases as the particle moves. The electric force and the displacement are in the same direction. Hence, the work done by the electric force is positive.

Now consider this question: What is the relationship between the the electric potential energy and the work done by the electric field on the particle? The bar graph should help you to see this relationship.