Question

The figure below is a section of a conducting rod of radius R1 = 1.30 mm and length L = 11.00 m inside a thick-walled coaxial conducting cylindrical shell of radius R2 = 10.0R1 and the (same) length L. The net charge on the rod is Q1 = +2.80 10-12C that on the shell is Q2 = ?4.00Q1. What is the magnitude E of the electric field at a radial distance of r = 2.00R2? [Example Prob: Book-Fundamentals of Physics, Chapter-23 & Problem-29]

Answer 1

The volume inside r = 1.5a is (4/3)pi*(1.5a)^3 - (4/3)pi * a^3 = (4/3)pi * 2.375a^3.
The charge inside that volume is ? times that.

The electric field is uniform, so the flux through the sphere of radius 1.5r is E * A = E * 4pi(1.5a)^2 = E * 4pi*2.25a^2

This equals Q/eps0, so E = [(4/3)pi * 2.375a^3 * ?] / [eps0 * 4pi * 2.25a^2] = (2.375/2.25) * a * ?/(3 eps0)

Your solution shouldn't have an r in it, since r is in terms of a. Nor should it have a b in it, since b is outside the sphere of radius r = 1.5a and therefo

Answer 2

For the first two parts of the problem, we use a Ganssian cylinder of radius 2R2. The total charge enclosed by this cylinder is Q +Q2-Q. We can now use Gauss's law to calculate the field -qi

Answer 3

E = 2 k (Q1 + Q2) / Lr = 2 * 8.99 x 109 * 3* 3.00 x10-12 / 11.0 * 20 * 0.0013 =
.
= 0.566 N/C
b) the point inwards
.
Part c:
.
E = 2 k Q1 / Lr = 2 * 8.99 x 109 * 3x10-12 / 11.0 * 4.5 * 0.0013 =
.
= 0.838 N/C
d) the direction is out ward
.
Part e: - 3 * 10-12C (i.e. the negative of Q1)
.
Part f: charge on outside + charge on inside = Q2
.
charge on outside - 3.00 x10-12 = 4 * -3x 10-12
.
chargeon outside = -9 x10-12