Write down an expression for the capacitance

Reference no: EM13977340

Consider a cylindrical capacitor (see figure 1) of length L and composed of two concentric cylinders: a solid inner conducing wire of radius r1, and an outer conducting shell with inner radius r2.

885_Cross Section of the Cylindrical Capacitor.png

The capacitance for this arrangement (you may consider the inner conductor to have a charge per unit length of +λ and the outer conductor to have a charge per unit length -λ) is derived in the text and is equal to

C = 2Πε₀L/ln( r₂/ r₁), (1)

where ε₀ is the permittivity of free space, and L is the length of the capacitor.

Now consider the following question, which are variations of this original situation.

1340_The Spase Between the conductor is filled with a dielectric.png

1. Single dielectric with constant k

Now we imagine taking the previous capacitor and completely filling the space with a dielectric as shown in Figure 2.

(a) The applied electric field from the existing positively charged inner conductor polarizes the dielectric and induces surface charge densities on the inner and outer surfaces of the dielectric. Assuming that we have a linear dielectric so that

E(r) = E₀(r) - E_induced(r) = E0(r)/k,

where E_induced is the electric field from the induced surface charge, derive an expression for the magnitude of the potential difference (ΔV) between the inner conductor and the outer shell.

b) Using the fact that C = Q/ΔV , write down an expression for the capacitance, C' .

Reference no: EM13977340

Questions Cloud

Which market structure would you classify airline industry : Under which market structure would you classify the airline industry? Given this structure, why is it that there is little price competition between carriers on the same route? Why is there not more price competition? If they do not choose to compete..

Use money just about every day : You use money just about every day. What is money and what functions does it perform? How is the supply of money measured? Who influences how much liquidity in created or reduced in the U.S. economy?

Find final velocity of each mass if the collision is elastic : A 20.0kg object moving in the +x direction at 6.5m/s collides head-on with a 13.0kg object moving in the- x direction at 5.5m/s . Find the final velocity of each mass if the objects stick together.

Constitution protects individual rights : You also learned that the government must balance the rights and needs of individuals with the needs of the public.

Write down an expression for the capacitance : Consider a cylindrical capacitor (see figure 1) of length L and composed of two concentric cylinders. Using the fact that C = Q/ΔV , write down an expression for the capacitance, C' .

The price of cappuccino relative to price of apple turnover : Eliza consumes 12 cappuccions and 8 apple turnovers per week. The price of cappuccinos is $4 each and apple turnovers are $1 each. what is the amount of income allocated to cappuccinos and apple turnover consumption? what is the price ratio(the price..

He factors, differentiate star performing district managers : he Factors that Differentiate Star Performing District Managers, In your final paper you will discuss the important factors or variables that differentiatethe Star Performing District Managers (DM's) from the non-Star Performing DM's.This paper will ..

Government is able to permanently reduce its budget : Suppose a government is able to permanently reduce its budget deficit. Use the Solow growth model to graphically illustrate the impact of a permanent government deficit reduction on the steady-state capita-labor ratio and the steady-state level of ou..

How is the preamble to the texas constitution different : Please submit the assignment prior to the deadline in the designated area (online textbox/no attachments). This needs to be submitted in an organized manner using complete sentences to answer each question and comparison. You can use essay format..

User Account

All Pages