Question

A co-axial cable is simply a conducting cylindrical shell which surrounds a line conductor. Suppose the outer shell has a charge line density (?) of 5.00 nC/m and a radius of 4.20 mm, while the line charge has a density of -2.00 nC/m. Assume both the shell and line are infinitely long.
A) Calculate the electric field halfway between the outer shell and the line charge (i.e. at 2.10 mm). (E = 1.71x104 N/C, inward)
B) Calculate the electric field 10.00 mm from the line charge. (5400 N/C, outward)

Answer 1

A) E = lamda1/(2*pi*epsiln*r)

= 2*k*lamda1/r

= 2*9*10^9*2*10^-9/(2.1*10^-3)

= 1.71*10^4 N/c

Here the direction of electric filed is radially inward Beacuse The charge charge on inner wire is neagative.

B) E = (lamda1+lamda2)/(2*pi*epsiln*r)

= 2*k*(lamda1+lamd2)/r

= 2*9*10^9*(-2+5)*10^-9/(10*10^-3)

= 5400 N/c

Here the direction of electric filed is radially outward Beacuse The net charge charge on both wire and cyllindrical shell is positive.