Question

In a solid uniformly charged sphere of total charge Q and radius R, if energy stored out side the sphere is U_(0) joules then find out self energy of sphere in term of U_(0) ?

Answer 1

Answer:

Self energy of sphere stored in it is given as 1.2 U_0

Explanation:

As we know that work done to charge the sphere uniformly from center to its surface is given as

$U = \int V dq$

here we know that V is the potential of the sphere of radius "r"

$V = \frac{k(\rho \frac{4}{3}\pi r^3)}{r}$

now we can integrate is for complete sphere

$U = \frac{3kQ^2}{5R}$

now we know that this is sum of energy stored inside the sphere and energy stored outside the sphere

So we have

$U = E_{out} + E_{in}$

also we know that the energy outside the sphere is given as

$U_0 = \frac{kQ^2}{2R}$

so we have

$\frac{kQ^2}{R} = 2U_0$

so we have

$U = \frac{3}{5}(2U_0)$

$U = 1.2 U_0$

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Topic : Self energy of sphere

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