A cylinder of length 195 m and radius 8.50 cm carries a uniform volume charge de

Question

A cylinder of length 195 m and radius 8.50 cm carries a uniform volume charge density of = 350 nC/m3.

(a) What is the total charge of the cylinder?
..... nC

Use the formulas given below to calculate the electric field at a point equidistant from the ends of following radial distances from the long axis of the cylinder.

Er = R2 / 20r = /20r, r > R
Er = r / 20 = r / 20R2, r < R
(where = R2 is the charge per unit length)

(b) r = 3.95 cm
.... N/C

(c) r = 8.44 cm
.... kN/C

(d) r = 8.56 cm
.... kN/C

(e) r = 12.8 cm
.... N/C

Explanation / Answer

here,

L = 195 m
r = 8.50 cm = 0.0850 m
= 350 nC/m^3 = 3.5*10^-7 C/m^3

Volume of cyclinder:
V = pi*r^2*h
V = 3.14 * 0.0850 * 195
V = 4.43 m^3

A)
as we know :
Volume charge Density = Charge / Volume of guassian surface
350 = Q / 4.43
Q = 350 * 4.43
Q = 1550.5 nC

Calculating :

= R2
= 3.5*10^-7 * 3.14 * (0.0850)^2
= 7.940 * 10^-9 C/m

B)
r = 3.95 cm = 0.0395 m
R = 0.0850 m
R >>>> r

Er = (*r) / (2*eo*R^2)
Er = (7.940 * 10^-9 * 0.0395)/(2*8.85*10^-12*0.0850^2)
Er = 2452.485 N/C

C)
r = 8.44 cm = 0.0844 m
R = 0.0850 m
R >>>> r

Er = (*r) / (2*eo*R^2)
Er = (7.940 * 10^-9 * 0.0844)/(2*8.85*10^-12*0.0850^2)
Er = 5240.247 N/C
Er = 5.240247 kN/C

D)
r = 8.56 cm = 0.0856 m
R = 0.0850 m
R <<<<< r

Er = /20r
Er = (7.940 * 10^-9)/(2*3.14*8.85*10^-12*(0.0856)^2)
Er = 19497.101 N/C
Er = 19.497101 kN/C

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.