Question

The energy of the system having two thin
concentric shells with charge as q1 and
q2 is​

Answer 1

Given:

Two thin concentric shells with charge as q1 and q2

To find:

The energy of the system having two thin concentric shells with charge as q1 and q2.

Solution:

From given, we have,

Two thin concentric shells with charge as q1 and q2.

Self-energy of each shell is given by,

Self-energy = qφ/2

where, φ is the potential of the shell, created only by the charge q, on it.

Hence, self-energy of the shells 1 and 2 are :

W₁ = q₁²/8πε₀R₂ and W₂=q₂²/8πε₀R₂

The interaction energy between the charged shells equals charge q of one, multiplied by the potential φ, created by other shells, at the point of location of charge q.

W₁₂ = q₁ q₂/4πε₀R₁

Hence, the total energy of the system,

U = W₁ + W₂ + W₁₂

∴ U = 1/4πε₀ [q₁²/2R₁ + q₂²/2R₂ + q₁q₂/R₂]