Question

An infinite long insulating cylinder (radius 12 cm) has a uniformly distributed charge of density p 5.0 nC/m3. Determine the electric field a.) 5.0 cm from the central axis of the cylinder. b.) On the surface of the cylinder c.) 15.0 cm from the central axis of cylinder

Answer 1

Since cylinder is insulating & infinite long therefor charge will spread in the entire volume of cylinder. Radius of cylinder R = 12 cm Part (a): Electric field inside the solid non conducting or insulating cylinder having volume charge density rho is given by E = rho r/2 epsilon_0 where r is the distance from central axis of cylinder where r < R In our case rho = 5 nC/m^3 & r = 5 cm. \r\n where epsilon_0 = permittivity of free space = 8.85 times 10^-12 C^2/Nm^2. Therefore E = 5.0 nC/m^2 times 5.0 times 10^-2 m/2 times 8.854 times 10^-12 C^2/N-m^2 E = 5 times 10^-9 times 5 times 10^-2/2 times 8.854 times 10^-12 (N/C) E = 25/2 times 8.854 times 10^-11 + 12 E = 250/2 times 8.854 = 28.23/2 N/C Therefore E = 28.23/2 N/C = 14.115 N/C Part (b): Electric field on the surface of cylinder (i.e. on r = R)