An infiinitely long solid conducting cylindrical shell of radius a = 2.7 cm and
ID: 1330718 • Letter: A
Question
An infiinitely long solid conducting cylindrical shell of radius a = 2.7 cm and negligible thickness is positioned with its symmetry axis along the z-axis as shown. The shell is charged, having a linear charge density inner = -0.46 C/m. Concentric with the shell is another cylindrical conducting shell of inner radius b = 17 cm, and outer radius c = 19 cm. This conducting shell has a linear charge density outer = 0.46C/m.
1)
What is Ex(P), the x-component of the electric field at point P, located a distance d = 8.4 cm from the origin along the x-axis as shown?
2.)
What is V(c) – V(a), the potential difference between the the two cylindrical shells?
3.)
What is C, the capacitance of a one meter length of this system of conductors?
Explanation / Answer
a)
here
Ex = 2 * k lambda(inner) / d
Ex= 2 * 9 * 10^9 * -0.46 * 10^-6 / 0.084
Ex = -9.85 * 10^4 N/C
b)
V(c) - V(a) = - 2 * k * lambda(inner) ln(b/a)
V(c) - V(a) = - 2 *9 * 10^9 * -0.46 * 10^-6ln(17/2.7) = 15234.9 V
c)
C = Q / V
Q / V = lambda * L / ( 2 * k * lambda * ln(b/a)
C = 1 / ( 2 * k * ln(b/a))
C = 1 / ( 2 * 9 * 10^9 * ln(17/2.7))
C = 3 * 10^-11 F