Question

A capacitor is formed from two concentric spherical conducting shells separated by vacuum. The inner sphere has radius 10.0cm , and the outer sphere has radius 16.0cm . A potential difference of 150V is applied to the capacitor.

1-What is the energy density at r = 10.1cm , just outside the inner sphere? (J/m^3)

2-What is the energy density at r = 15.9cm , just inside the outer sphere?

Answer 1

To resolve this problem you have to know about Gauss's law

Step 1:

Definition: In physics Gauss's law , also known as Gauss theorem states that certain fields flow through a closed surface is proportional to the magnitude of the sources of the field at the inside of said surface. These fields are those whose intensity decreases as the distance from the source squared. The proportionality constant depends on the system of units used.

Step 2:

ANSWERS:

Apply the gauss's law from two concentric spherical, we have the following

    

;

To calculate of the energy density, we have use the following equation

  Replace the electric field for the equation of electric field above

The energy density for r =10.1 cm

Now the energy density per unit of volume

The energy density for r =15.9 cm

Now the energy density per unit of volume

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