The Potential Difference Due to
Continuous Charge Distributions
A ring of charge has a total charge of Q = 20 µC (or 20 ´ 10-6 C). The radius of the ring, a, is 30 cm. We wanted to
find the electric field, E, at a distance of x cm from the ring along an axis that is perpendicular to the ring
and passing through its center and the potential, V. First we divided the
ring into 20 pieces of charge Dq and calculated the total V at a distance of x = 20 cm from the center of the ring using a spreadsheet
program. We calclulated the potential
difference to be 4.7 x 10 ^ 5. We then integrated to find a more exact value of
the total potential difference. We
determined that the potential difference was 4.9 x 10 ^ 5. There is a 4.16% difference between the two
values which is due to the face that we only split the ring into 20 pieces when
calculating it whereas the integral takes an infinite amount of pieces and sums
them.Electric Potential due to a finite-length line-charge
A 16.0 cm long, horizontal rod has a uniform charge density
of 2.70 mC/cm. Taking the left end of
the rod to be the origin determine the electric potential at the point (10.0
cm, 15.0 cm). First we divided the bar
into 17 equal pieces from .005 m to .165m and calculated the electric potential
by using the equation kq/r where r = sqrt((a-x)^2+b^2) for each of the 17 pieces and then summed them
up to get the total electric potential of 2.63 kV We then calculated the electric potential by
integrating. We found that value to be 2.47kV.
Electric Potential
Lab/Activity
See pictures
 |
| solving V/m & V/cm |
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