Homework: HW8 of CH22 Thip Tipler6 22.P.049. Tip A cylindrical shell of length 2

Question

Homework: HW8 of CH22 Thip Tipler6 22.P.049. Tip A cylindrical shell of length 208 m and radius 6 cm carries a uniform surface charge density of 0-13 nC/ Tip What is the total charge on the shell? You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question Find the electric field at the ends of the following radial distances from the long axis of the cylinder. r=3cm You currently have 0 submissions for this question. Only 10 submission are allowed You can make 10 more submissions for this question. +5.9 cm You currently have 0 submissions for this question. Only 10 submission are allowed You can make 10 more submissions for this question. r-6.1 cm You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question. 5, r = 10 cm You currently have 0 submissions for this question. Only 10 submission are allowed. You can make 10 more submissions for this question.

Explanation / Answer

Given

cylindrical shell of length l = 208 m , radius r = 6 cm= 0.06 m

with uniform surface charge density is sigma = q/A = 13 nc/m^2

now total charge on the shell is Q = A*sigma = 2pir(r+l)*sigma

Q = 2pi*0.06(0.06+208)(13*10^-9) C

Q = 1.01967*10^-6 C

2. we know that from definition of electric flux and Gauss law  

phi = E*A cos theta = Q_in/(epsilon not)

==> E = Q_in/(epsilon not*A cos theta)

given R = 3 cm

==> Q_in = 2pi*R*L*sigma

E= Q_in/epsilon not

E = 2pi*R*l*sigma / epsilon not

E = 2pi*0.03*208*13*10^-9 /(8.854*10^-12) N/C

E = 57566.3 N/C

3.E at R = 5.9 cm is  

==> Q_in = 2pi*R*L*sigma

E= Q_in/epsilon not

E = 2pi*R*l*sigma / epsilon not

E = 2pi*0.05*208*13*10^-9 /(8.854*10^-12) N/C

E = 95943.83 N/C

4. R = 6.1 cm , which is at out side of the cylinder from Gauss law  

the electric field is E = Q_in/(A*epsilon not)

here Q_in = 0

so E(6.1 cm) = 0 N/C

5. R = 10 cm

againg the position is out of the cylinder where the contribution of charge is zero so

E(10cm) = 0 N/C

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