4. Examine the electric field and charge distribution of a 1-meter long section

Question

4. Examine the electric field and charge distribution of a 1-meter long section of two nested conducting cylinders. The interior cylinder has a radius of 1cm and a total charge of +2 mu C. The outer cylinder has an inner radius of 3 cm and outer radius of 4cm. It has a charge of -1 mu C. Assume that Gauss? law can be used (the field is uniform and perpendicular to the cylinders). The surface area of a hollow cylinder is 2 pi r L where r is the radius and L is the length. a. What is the electric field 2cm from the center of the inner cylinder? Include the direction (toward or away from the cylinder). b. What is the electric field 5cm tram the center? Include the direction (toward or away from the cylinder). c. How much of the outer shell's charge is on the inside surface and outside surface?

Explanation / Answer

a) charge per unit length on inner cyllinder, lamda_i = Q_in/L

= 2*10^-6 C/m

E = lamda_i/(2*pi*epsilon*r)

= 2*lamda/(4*pi*epsilon*r)

= 2*k*lamda/r

= 2*9*10^9*2*10^-6/2*10^-2

= 1.8*10^6 N/c

b) charge per unit length on ounter cyllinder, lamda_o = Q_out/L

= -1*10^-6 C/m

E = E = (lamda_i+lamda_o)/(2*pi*epsilon*r)

= 2*(lamda_i+lamda_o)/(4*pi*epsilon*r)

= 2*k*(lamda_i+lamda_o)/r

= 2*9*10^9*(2*10^-6 - 1*10^-6)/5*10^-2

= 3.6*10^5 N/c

c) charge on inner surface of outer cyllinder = -2 micro C

charge on outer surface of outer cyllinder = +1 micro C

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