This document discusses electrostatics and electric potential through 5 sample problems. It outlines the general steps to take in solving for the electric field or potential. These include: 1) writing the equation, 2) determining charge density, 3) substituting the charge element, 4) integrating, 5) substituting total charge density, and 6) plugging in ranges and simplifying. The document explains how these steps remain the same but the specifics change depending on the geometry and properties of the situation.

1. Electrostatics
&
Electric Potential
5 Sample Problems

2. P
1. Point Charges
+
-
+

4. 2. Rod (E) P a
L
• Find the Electric Field
@ point P.
1. Equation
2. Since r and q
change together, we
need an equation that
relates the two.
Charge Density. The
3. Solve for dq and substitute it in. density stays constant
Pull your constants out of the integral. whether over the
Determine the range and place it on total charge or parts
the integral. of the rods.

5. 2. Rod (E) P a
L
• Find the Electric Field
@ point P.
a+L
4. Integrate.
a
a+L
5. Substitute in the
a total charge density.
6. Plug in the ranges
and simplify.

6. 2. Rod (V) P a
L
• Find the Electric Potential
@ point P.
1. Equation
2. Since r and q change
together, we need an
equation that relates
the two.
Charge Density. The
3. Solve for dq and substitute it in. Pull density stays constant
your constants out of the integral. whether over the
Determine the range and place it on total charge or parts
the integral. of the rods.

7. 2. Rod (V) P a
L
• Find the Electric Field
@ point P.
a+L
4. Integrate.
a
a+L 5. Substitute in the
total charge density.
a
6. Plug in the ranges
and simplify.

8. Notice that the steps for solving were the same in
both cases.
In all the different problems, those steps stay the
same. The only thing that changes is how you do
the step. For instance, how you integrate, or
whether you use linear charge density, area
charge density, or volume charge density, etc.

10. 3. Ring (E) a
P
• Find the Electric Field x
@ point P.
1. Equation
2. Don’t need charge
density because all
the charges are
equidistant adding
the same values to
the field.
or a & x are constant.
3. Replace dq. Pull out constants. Set Range.

11. 3. Ring (E) a
P
• Find the Electric Field x
@ point P.
4. Integrate.
5. No charge density to
substitute!
6. No range since you
will probably know
the total charge.

12. 3. Ring (V) a
P
• Find the Electric x
Potential @ point P.
1. Equation
2. a & x are constants!
3. Replace dq. Pull out
constants. Set Range.
4. Integrate.
5. No charge density to
substitute!
6. No range since you
will probably know
the total charge.

14. 4. Disk (E) r
P
• Find the Electric Field x
@ point P.
1. Equation
2. Charge Density. Area
because we’re moving
out concentric circles.
3. Replace dq. Pull out constants. Set Range.

15. 4. Disk (E) r
P
• Find the Electric Field x
@ point P.
4. Integrate.
R
0
5. Substitute in the
R total charge
0 density.
6. Plug in the ranges
and simplify.

16. 4. Disk (V) r
P
• Find the Electric x
Potential @ point P.
1. Equation
2. Charge Density:
Area Again
3. Replace dq. Pull out constants. Set Range.

17. 4. Disk(V) r
P
• Find the Electric Field x
@ point P.
4. Integrate.
R
0
6. Plug in the ranges
and simplify.

19. 5. Arc Length (E) r
P
• Find the Electric Field x
@ point P.
1. Equation
(cos because all the y
values cancel out.)
2. Charge Density.
θ changes with respect
to the arc length!
3. Replace dq. Pull out constants (r is constant!). Set Range.

20. 5. Arc Length (E) r
P
• Find the Electric Field x
@ point P.
4. Integrate.
5. Substitute in the
total charge density.
6. Plug in the ranges
and simplify.
7. The length is
the arc length.

21. 5. Arc Length (V) r
P
• Find the Electric Field x
@ point P.
1. Equation
2. Charge Density.
3. Replace dq. Pull out constants (r is constant!). Set Range.
θ changes with respect to the arc length!
Must be in Radians though (since θ is not in a function.)

22. 5. Arc Length (V) r
P
• Find the Electric Field x
@ point P.
4. Integrate.
5. Substitute in the
total charge density.
6. Plug in the ranges
and simplify.
7. The length is
the arc length.