Consider a conducting ball of radius a, charged with charge Q, surrounded by air and located...

  

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Consider a conducting ball of radius a, charged with charge Q, surrounded by air and located far from other objects: 2) Starting from the general expression for the electric field energy density at any point of space W =8², derive an expression for the total energy stored in the entire space by evaluating the integral: Wfield All space wd³ v. Express the final result solely in terms of variables a and Q. (Hint: use spherical coordinates, well know result for the field strength inside and outside the ball, and multivariate integration.) b) Starting from the formula for the energy stored in a capacitor Wetrcuit QV, use the well known result for the electric potential on the surface of a ball to express Weircuir solely in terms of variables a and Q. c) Verify that the field point of view and circuit point of view produce identical results for the electrical energy of a charged ball. Consider a conducting ball of radius a, charged with charge Q, surrounded by air and located far from other objects: 2) Starting from the general expression for the electric field energy density at any point of space W =8², derive an expression for the total energy stored in the entire space by evaluating the integral: Wfield All space wd³ v. Express the final result solely in terms of variables a and Q. (Hint: use spherical coordinates, well know result for the field strength inside and outside the ball, and multivariate integration.) b) Starting from the formula for the energy stored in a capacitor Wetrcuit QV, use the well known result for the electric potential on the surface of a ball to express Weircuir solely in terms of variables a and Q. c) Verify that the field point of view and circuit point of view produce identical results for the electrical energy of a charged ball.

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a The electric field inside a uniformly charged conducting spherical shell ... View the full answer