You are presented with a coaxial cable of length L. The inner core has a uniform

Question

You are presented with a coaxial cable of length L. The inner core has a uniform charge distribution throughout its radius and length of total charge Q. It is surrounded by and insulating sheath of a thinkness that is 1/6 of the radius of the inner core. Surrounding that is an outer material that has a thickness that is 1/2 of the radius of the inner core that has a uniform charge distribution throughout its radius and lenght of total charge -Q/3. Finally, there is an insulating sheath that has a thickness that is 1/6 of the radius on the inner core .

a) Find the electrostatic potential in all radial regions(ignore end effect at the ends of the wire)

b)Find the electric field in all radial regions (ignore end effects at the ends of the wire)

Explanation / Answer

inner core has a uniform charge distribution throughout its radius and length of total charge Q

according to gauss law flux through closed surface=charge enclosed

first we need to determine electricfield due to CHARGE Q

E=Q*/2*3.14*epsilon*r*L

for relative permittivity k. so to cover the whole radius,

=Q*/2*3.14*epsilon*r*K*L

E(r) = q/(2*pi*k1*epsilon0*L*r) for r1*0.16 <= r < r1

E(r) = q/(2*pi*k2*epsilon0*L*r) for 0.5r1 <= r < c<r1

inorder to determine the potential integrate from where the charge is to be brought

V=-(integration of electricfield between given limits)

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