You are working with a team designing capacitors for specialized purposes. One client needs a capacitor...

You are working with a team designing capacitors for specialized purposes. One client needs a capacitor shaped like a sphere that can store the most energy for its size. You are to begin the design process by performing calculations for a simple spherical capacitor consisting of two thin concentric spherical shells separated by a dielectric. You decide to calculate the maximum energy that can be stored in terms of the radius of the outer shell and the maximum electric field that the dielectric can withstand before breaking down.

After you have derived a symbolic answer, get an idea of how much energy this is by finding a numerical answer for a capacitor with an outer shell that has a radius of 5 cm (about the size of a softball), filled with a dielectric with a breakdown voltage of 150 x 10⁶ V/m and a dielectric constant of 3.

(a) Give a purely symbolic answer to the problem in terms of (only) the quantities given in the problem and known constants. Be sure to define each of the symbols you use.

(b) Give a numerical answer to the problem.

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Expert Solution

genius_generous answered 1 year ago

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