1. Electric Fields
AP Physics C

2. Electric Fields The field model describes how charges interact:
A group of charges, which we will call the source charges, alters the space around them by creating an electric field E.
If another charge is then placed in this electric field, it experiences a force F exerted by the field.
The electric field is most basically defined as:
𝐸= 𝐹 𝑞
We can see that an electric field describes the amount of force per unit charge on a charged object or particle.
The SI units of electric field are Newtons per Coulomb (N/C).
The “q” in the equation is that of a “test charge”.

3. Electric Field of a Point Charge
The simplest model of an electric field is that of a point charge.
Using Coulomb’s law and our formula for electric field, we can determine the electric field strength of a point charge:
𝐸 𝑝𝑜𝑖𝑛𝑡 𝑐ℎ𝑎𝑟𝑔𝑒 = 𝑘𝑄 𝑟 2 = 1 4𝜋 𝜀 𝑜 𝑄 𝑟 2
This shows that the electric field strength drops off as an inverse square function, just like electric force.
Also, notice that the electric field is dependent on the point charge, not the test charge.
Positive point charges produce a field that points radially outward, negative charges point radially inward.

4. Uniform Electric Fields
A uniform electric field is one in which the field strength is constant and the field lines are parallel to one another.
No real field is uniform, but the field between two oppositely charged plates is fairly close.

5. Electric Field of a Dipole
The electric field of a dipole can be found by combining the electric fields of both particles.
If you place a dipole in a uniform external electric field, the dipole will align with the field, but it will not have a net force acting on it.

6. Example
An electron is placed at rest in an external electric field of 520 N/C. Calculate the speed of the particle after 48 ns.
4.38 x106 m/s

7. Example 0.899 N/C to the right
A -4 x10-12 C charge Q is placed at the origin. What is the magnitude and direction of the electric field produced by Q if a test charge were placed at x = -0.2 m ?
0.899 N/C to the right

8. Electric Fields and Superposition
Electric fields are vectors, and thus they obey the principle of superposition.
If you have a collection of charged particles, you can find the electric field at some point by adding the electric fields created by each particle.
You may have to break each field into its x and y components to do this!
𝐸= 𝑘𝑞 𝑟 2

9. Example
Determine the magnitude and the direction of the electric field at point A.

10. Electric Fields of Charge Distributions
All we have done so far has been dealing with specific points in space. What if we are dealing with an object that has a continuous amount of charge over its surface?
In this case, we take the object and slice it into an infinite number of pieces, each with an infinitesimal amount of charge on it, dq.
We take our formula for the field due to a point charge and modify it:
𝐸= 𝑘𝑄 𝑟 2 𝑑𝐸= 𝑘𝑑𝑞 𝑟 2
You can take this function and integrate it over the appropriate bounds to find the total electric field.
This can be rather complicated, and often is completely unnecessary. We will find other methods to accomplish this task.