Consider a pair of nested, conducting spheres: Figure 2: Problem 3 The inner sph

Question

Consider a pair of nested, conducting spheres: Figure 2: Problem 3 The inner sphere has a radius of a, the outer sphere has a radius of b. You are told that a charge of +Q is placed on the inner sphere, and-Qis placed on the outer one. (a) Calculate the capacitance of this system. How much energy is stored in this capacitor? (b) How would your answers to (a) change if the space between the shells was filled with a dielectric with given dielectric constant ke? For the remainder of the problem, assume that b 2a and that there is not dielectric Careful measurements establish that the electric field in the region a fact obey the rule you found in part (a). (The electric field in agrees with with your measurement in part a).) Instead, we find

Explanation / Answer

a) For region a<r<b , E = kQ/r2

Finding the potential difference between two shells

V = - kQ (1/a - 1/b) WHERE k = 1/4*pi*Eo

V = -kQ (b - a / ab)

Now, use the formula

Q = CV

C = Q/ |V|

C = 4?Eo (ab / b-a)

Energy stored, U = 1/2*C*V2

U = 1/2 * Q / 4?Eo * b-a / ab

b) If the space is filled with dielectric with dielectric constant Ke

then CNEW = KeC

CNEW = Ke4?Eo (ab / b-a)

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