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Question:

Spherical capacitance, C, is defined as the ratio of the product of 4, π, vacuum permittivity, $2437_w13_h11.png$, and Coulomb's constant, k to the difference between the ratio of 1 to the radial length a, and the ratio of 1 to the radial length b. Which of the following correctly solves spherical capacitance for radial length b?

A $4198_w124_h39.png$
Explaination

Begin by translating the given definition into an algebraic expression. $4259_w85_h45.png$ Manipulate the equation to solve for b: Multiply both sides by the denominator: $7111_w143_h37.png$, divide both sides by C: $4669_w117_h38.png$, solve for $3930_w9_h37.png$ $2056_w117_h38.png$, combine the right hand side using the common denominator: $5319_w127_h38.png$, and evaluate the reciprocal of each side to find b: $2349_w124_h39.png$