Gauss\'s Law A long, solid, cylindrical, insulating rod of radius R has a unifor

Question

Gauss's Law

A long, solid, cylindrical, insulating rod of radius R has a uniform charge density . Ccoaxial with this solid rod is a metallic, hollow cylinder of inner radius a and outer radius b. The hollow cylinder is also charged, it carries a linear charge density of .

A. What is the electric field inside the material of the hollow cylinder <a<r<b)?

B.How does this help one to determine how the charges are distributed on the hollow cylinder?

C. What is the surface charge density on the inner surface of the hollow cylinder?

D. What is the surface charge density on the outer surface of the hollow cylinder?

Explanation / Answer

Here ,

as the hollow cyclinder is metallic ,

it will be conducting

as the electric field inside a conductor is zero

for a < r < b

the electric field inside the material of the hollow cyclinder is zero

B)

the sum of charges on the inner side and the rod must be zero accroding to above result

c)

let the surface charge density is sigma

sigma * pi * 2a * L = - p * pi * R^2 * L

sigma = -p * R^2/(2a)

where p is the uniform charge density of insulator

the surface charge density on the inner surface of the hollow cyclinder is -p * R^2/(2a)

D)

surface charge density on the outer surface = ( * L + (p * R^2/(2a)) * 2*pi * a * L )/(2 *pi*b*L)

surface charge density on the outer surface = ( + (p * R^2/(2a)) * 2*pi * a)/(2 *pi*b)

the surface charge density on the outer surface is ( + (p * R^2/(2a)) * 2*pi * a)/(2 *pi*b)

Related Questions

Navigate

• Browse (All)
• Browse G
• Subjects

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