Charge is distributed uniformly throughout the volume of an infinitely long cyli

Question

Charge is distributed uniformly throughout the volume of an infinitely long cylinder of radius R = 12 cm. The volume charge density is 5.7 nC/m3. Find the magnitude of the electric field E (a) inside the cylinder, a distance r = 2.4 cm from the cylinder axis, and (b) outside the cylinder, a distance r = 16 cm from the cylinder axis.

(a) Number Enter your answer for part (a) in accordance to the question statement Units Choose the answer for part (a) from the menu in accordance to the question statement ° (degrees)This answer has no unitsmkgsm/sm/s^2NJWN/mAVCN/CC/mC/m^2C/m^3N·m^2/C

Explanation / Answer

part(a)

consider a gaussian cylinder of radius r and length l

volume of gaussian sphere V = pi*r^2*l

charge inside the gaussian sphere q = rho*V = rho*pi*r^2*l

rho = charge density

surface area of sphere A = 2*pi*r*l

flux through surface = E*A = E*2*pi*r*l

from gauss law

flux = q/epsilon0

E*2*pi*r*l = rho*pi*r^2*l/e0

E = rho*r/(2*e0)

E = 5.7*10^-9*0.024/(2*8.85*10^-12)

E = 7.73 N/C

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part(b)

r > R

consider a gaussian cylinder of radius r and length l

charge inside the gaussian sphere Q = rho*Vsphere = rho*pi*R^2*l

rho = charge density

surface area of sphere A = 2*pi*r*l

flux through surface = E*A = E*2*pi*r*l

from gauss law

flux = q/epsilon0

E*2*pi*r*l = rho*pi*R^2*l/e0

E = rho*R^2/(2*r*e0)

E = 5.7*10^-9*0.12^2/(2*0.16*8.85*10^-12)

E = 29.8 N/C

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