Question

A sphere of radius r has a charge q distributed uniformly over its surface. How large a sphere contains 90 percent of the energy stored in the electrostatic field of this charge distribution?.

Answer 1

r = 10R large a sphere contains 90 percent of the energy stored in the electrostatic field of this charge distribution.

What is the use of electrostatic field?

As charges move from positive to negative, electric field lines follow. These sources are ideal for surface applications including corneal restoration, wound healing, and even brain and spinal stimulation using thin, implanted electrodes.

Briefing:

The sphere's surface has an electric field that is:

$E=k \frac{Q}{R^2}$

Electric energy density is  $\frac{1}{2} \epsilon_0 E^2$

If 'r' be the radius of the sphere containing 90% of this energy

$U=\int_0^r \frac{1}{2} \epsilon_0 E^2\left(4 \pi r^2\right) d r$

$U=2 k Q^2 \int_0^r \frac{d r}{r^2}=2 k Q^2\left(1-\frac{R}{r}\right)$

for r= infinity we get

Given

U/U$_t_o_t_a_l$ = 0.9

(1 - R/r) = 0.9

r = 10R

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