Answered: "An isolated conducting Sphere of radius R has..."

High School
Physics
Electromagnetism
Magnetism

Makena Preston

Answered question

2022-07-17

An isolated conducting Sphere of radius R has a charge Q. What is the total stored energy? What is the radius r within which half the stored energy is contained?

Answer & Explanation

Marisa Colon

Beginner2022-07-18Added 18 answers

The energy stored in conducting sphere of radius R is

U = \frac{1}{2} Q V

Q=charge stored
V=potential at R distance

∴ U = \frac{1}{2} Q \cdot \frac{Q}{4 π ϵ o R^{2}} = \frac{Q^{2}}{8 π ϵ o R^{2}}

assuming for r radius the stored energy is

U^{'} = \frac{U}{2}

then,

\frac{Q^{2}}{8 π ϵ o R^{2}} = \frac{1}{2} \frac{Q^{2}}{8 π ϵ o R^{2}} \Rightarrow r = \sqrt{2} R

radius is

\sqrt{2} R

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