Question 1( 10 pts) consider an infinite line of charge, of charge density = 104

Question

Question 1( 10 pts) consider an infinite line of charge, of charge density = 104c/m. Find the flux through a cylindrical shell of length L-10 cm and radius R- 1 cm. Assume that the axis of the cylinder and the line of charge coincide 10-6 What is the flux through the flat end faces of the cylinder? (Hint: What is the direction of the normal to these faces and what is the direction of the Electric field due to the line?) Calculate the flux through the curved part of the cylinder and hence the total flux through the cylinder. a) b)

Explanation / Answer

flux is phi = E*A*cos(theta)

theta is the angle between A and E

a) at the flat faces the angle between E and A is 90 degrees

so phi = E*A*cos(90) = 0 N-m^2/C

b) through curved part ,the Field E and A are in same direction,hence the flux is phi = E*A

A is the surface area of the cylinder= 2*pi*R*L

E = lamda/(2*pi*eo*R)

then

Phi = E*A = [lamda/(2*pi*eo*R)]*(2*pi*R*L)

phi = lamda*L/eo

eo is the permittivity of free space

then phi = lamda*L/eo = (10^-6*10*10^-2)/(8.85*10^-12) = 11300 Nm^2/C

hence total flux through the cylinder is Phi = 11300 N m^2 /C

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