Question

Can you do problem 4

Consider the figure above in scenario A: It is connected to the battery with potential difference V0. Ignore fringe effects. What is the condition under which this system behaves like an ideal parallel-plate capacitor? Express the relation in terms of A and D. Derive the formula for capacitance for the parallel-plate configuration. Find the capacitance if A = (1 cm)2, D = 1 mm, and V0 = 10 V. Consider the figure above in scenario B: After scenario A, it is disconnected and the plates are separated by external force, keeping the charges constant, until the separation is 2D. Express the answers symbolically using some or all of the following symbols: A, D, epsilon0, and V0. Write the expression for the potential difference. Write the expression for the initial and final stored energy in the capacitor. Write the expression for the work required by the external force to move the plates from D to 2D.Follow-up of the cylindrical capacitor done in class. You will show that under the condition expressed in Problem 2a above, the cylindrical capacitor looks like a parallel plate capacitor. Rewrite the capacitance by expressing the larger radius as b = a + delta. Expand the capacitance to O(delta) given that delta/a << 1. Should look like a parallel-plate now.

Answer 1

For a cylindrical geometry like a coaxial cable, the capacitance is usually stated as a capacitance per unit length. The charge resides on the outer surface of the inner conductor and the inner wall of the outer conductor. The capacitance expression is

In a) C= L (2$\pi \kappa \epsilon$)/(ln(a+$\delta$)/a) = L(

C= L(2$\pi \kappa \epsilon$)/ln$\delta$