All AP Physics C Electricity Resources
Example Questions
Example Question #21 : Electricity And Magnetism Exam
Three equal point charges are placed at the vertices of an equilateral triangle of side length
. Calculate the potential at the center of the triangle, labeled P.
Draw a line from the center perpendicular to any side of the triangle. This line divides the side into two equal pieces of length . From the center, draw another line to one of the vertices at the end of this side. This produces a 30-60-90 triangle with longer leg
, so the hypotenuse (the distance from the vertex to the center) is
. The potential at the center is due to three of these charges, so it must be
Example Question #23 : Electricity And Magnetism Exam
A uniformly charged hollow disk has inner radius and outer radius
, and carries a total charge
. Calculate the potential a distance
from the center, on the axis of the disk.
Use a polar coordinate system with surface charge density and area element
. The distance from the point of interest to a point a distance
from the center is
, so the potential is
Example Question #23 : Electricity And Magnetism Exam
Two point charges and
are separated by a distance
. Calculate the potential at point P, a distance
from charge
in the direction perpendicular to the line connecting the two charges.
By the Pythagorean theorem, the distance from point P to charge is
. Because point P is also
from charge
, it follows that the potential is
Example Question #24 : Electricity And Magnetism Exam
A nonuniformly charged ring of radius carries a linear charge density of
. Calculate the potential at the center of the ring.
Use a polar coordinate system, the given linear charge density , and length element
. Since every point on the ring is the same distance
from the center, we calculate the potential as
Example Question #24 : Electricity And Magnetism Exam
In this model of a dipole, two charges and
are separated by a distance
as shown in the figure, where the charges lie on the x-axis at
and
respectively. Calculate the exact potential a distance
from the origin at angle
from the axis of the dipole.
By the law of cosines, the distance from the point to charge is
.
The distance to charge can be found by using the law of cosines using the supplementary angle
, for which
. Therefore the distance to
is
.
Lastly, the exact potential is given by
.
Remark: Far from the dipole (approximating ) gives the much simpler equation for the potential of an ideal electric dipole
.
Example Question #25 : Electricity And Magnetism Exam
A uniformly charged hollow spherical shell of radius carries a total charge
. Calculate the potential a distance
(where
) from the center of the sphere.
Use a spherical coordinate system and place the point of interest a distance from the center on the z-axis. By the law of cosines, the distance from this point to any point on the sphere is
. Using surface charge density
and area element
, we evaluate the potential as:
.
Remarkably, this is the same potential that would exist a distance from a point charge.
Example Question #181 : Ap Physics C
A thin bar of length L lies in the xy plane and carries linear charge density , where
ranges from 0 to
. Calculate the potential at the point
on the y-axis.
Use the linear charge density and length element
, where each point is
from the point
. The potential is therefore
Example Question #182 : Ap Physics C
A uniformly charged ring of radius carries a total charge
. Calculate the potential a distance
from the center, on the axis of the ring.
Use the linear charge density and length element
. The distance from each point on the ring to the point on the axis is
. Lastly, integrate over
from
to
to obtain
Example Question #183 : Ap Physics C
A uniformly charged square frame of side length carries a total charge
. Calculate the potential at the center of the square.
You may wish to use the integral:
Calculate the potential due to one side of the bar, and then multiply this by to get the total potential from all four sides. Orient the bar along the x-axis such that its endpoints are at
, and use the linear charge density
. The potential is therefore
All AP Physics C Electricity Resources
