A long pipe of outer radius 3.50 cm and inner radius 2.98 cm carries a uniform c

Question

A long pipe of outer radius 3.50 cm and inner radius 2.98 cm carries a uniform charge density of 4.22 mC/m3. Using Gauss's law and assuming the pipe is sufficiently long to consider it infinitely long, calculate the electric field r = 7.35 cm from the centerline of the pipe.

A long pipe of outer radius 3.50 cm and inner radius 2.98 cm carries a uniform charge density of 4.22 mC/m3. Using Gauss's law and assuming the pipe is sufficiently long to consider it infinitely long, calculate the electric field r= 7.35 cm from the centerline of the pipe. Side view Top view Number R2 5.05 × 105 N/C Incorrect.

Explanation / Answer

By Gauss’s law :

0EA = Q => E=Q/ 0A

Here A= 2rL

Q=Charge density*volume of the pipe = Charge density*area of shell*length of pipe

Q=*(R12-R22)L

Hence E= (*(R12-R22)L)/( 02rL) = (/ 20r)* *(R12-R22)

Plugging values,

E= (4.22*10^-3/(2*8.85*10^-12*0.0735))*(0.035^2-0.0298^2) = 1.09*10^6 N/C

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