II. Uniform infinite cylinder of charge. Consider an infinite insulating cylinder with radius R, length L and volume charge density po. You will derive its electric field using Gauss' Law for regions inside (r < R) and outside (r>R). a. Draw the appropriate Gaussian surfaces for the charge distribution (1 each for r < R and r > R). How much charge is enclosed by each surface? Hint: Qencl=pV r < R r > R b. Write the total electric flux through the surfaces in terms of the enclosed charge r R C. Write the total electric flux using the general definition of electric flux. (E = $ Ē. dA) r< R r> R d. By equating your answers in B and C, write down the magnitude of the electric field generated by the infinite cylinder. T R
II. Uniform infinite cylinder of charge. Consider an infinite insulating cylinder with radius R, length L and volume charge density po. You will derive its electric field using Gauss' Law for regions inside (r < R) and outside (r>R). a. Draw the appropriate Gaussian surfaces for the charge distribution (1 each for r < R and r > R). How much charge is enclosed by each surface? Hint: Qencl=pV r < R r > R b. Write the total electric flux through the surfaces in terms of the enclosed charge r R C. Write the total electric flux using the general definition of electric flux. (E = $ Ē. dA) r< R r> R d. By equating your answers in B and C, write down the magnitude of the electric field generated by the infinite cylinder. T R
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Transcribed Image Text:II. Uniform infinite cylinder of charge. Consider an infinite insulating cylinder with radius R, length L and volume
charge density po. You will derive its electric field using Gauss' Law for regions inside (r < R) and outside
(r>R).
a. Draw the appropriate Gaussian surfaces for the charge distribution (1 each for r < R and r > R).
How much charge is enclosed by each surface?
Hint: Qencl=pV
r < R
r > R
b. Write the total electric flux through the surfaces in terms of the enclosed charge
r<R
r > R
C. Write the total electric flux using the general definition of electric flux. (E = $ Ē. dA)
r< R
r> R
d. By equating your answers in B and C, write down the magnitude of the electric field generated by
the infinite cylinder.
T<R
r > R
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