ahle to use Casslaw so find the electric felds of charged sphere, cylimdex, pane

Question

ahle to use Casslaw so find the electric felds of charged sphere, cylimdex, pane, or ey lismdrical shel. ectric potential energy U-U--w. U--w ectric potential v- loulating potential from field v--f·E-di v-v-- · field froen potetial: Ev ial energy: For two charges U -, for mukiple charges U potential of comtinuous charge v- to find the elestric potential at a point by muhiple changes: he able to find the pesential of charged rod, and disk calculate the potential energy of a point charge sy stem 2. (30 pts) (1) Given the electric flux into the cylinder side surface to 8 Nm2/C and out of the cylinder top and bottom surfaces to be 6 and 4 Nm/C, respectively. Find the electric charge inside the cylinder. (2) For a long cylinder with a radius of 10 em and is uniformly charged with the charge line density 100 nC/m, what is the electric field inside the cylinder at a point with the radial distance of 4 cm from the axis?

Explanation / Answer

2. (1) total flux = - 8 + 6 + 4 = 2 N m^2 / C

from Gauss law, net flux = Qin / e0

2 = (Qin) / (8.854 x 10^-12)

Q = 17.7 x 10^-12 C

2) from Gauss law for long cylinder,

E ( 2 pi r L ) = Qin / e0

Qin = lambda L r^2 / R^2

E (2 pi r L ) = ( lambda L r^2 / R^2) / e0

E = lambda r / (2 pi e0 R^2)

E = (100 x 10^-9)(0.04) / (2 x pi x 8.854 x 10^-12 x 0.10^2)

E = 7190.2 N/C

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