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## Homework Statement

Assume a conducting sphere has a radius of 3400km with an electric field of 100 V/m at it's surface.

a) Calculate total charge of sphere.

b)Calculate potential at the surface using infinity at reference point

c) Calculate capacitance of the sphere using the result of a or b but not both.

I know how to do all the problems but how do I go about doing part C while using only one of the results?

## Homework Equations

-Gauss's Law

-Potential

-Capacitance

## The Attempt at a Solution

a)

$$\oint E.dA = \frac{q}{\epsilon_0}$$

$$q = E(4\pi*R^2)\epsilon_0$$

$$q=100*4\pi*(3.6*10^5)$$

$$1.63*10^{14} Coulombs$$

b)

$$V(r) = -\int E.dl$$

$$= -\frac{q}{4\pi\epsilon_0} \int_\infty^R \frac{1}{r^2}dr$$

$$=\frac{q}{4\pi\epsilon_0 R}$$

$$=\frac{1.63*10^{14}}{4\pi\epsilon_0(3.6*10^5)}$$

$$4.07*10^{28} J$$

c) $$C = \frac{Q}{\Delta V}$$.

I have no idea how to appraoch it using only variable. I know the answer must be Q/V from a and b.

Thank you for any guidance.

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