Question

Q. A spherical capacitor of inner radius $R_1$ and outer radius $R_2$ is filled with an inhomogeneous dielectric having $\epsilon = \epsilon_0 R$, where $\epsilon_0$ is the permittivity of the vacuum and R is radial distance. Assume that $V = V_0$ on the inner sphere and $V = 0$ on the outer sphere. a) By using Laplace equation find $\vec{D}$ and $\vec{E}$. b) Find $\rho_s$ on the inner sphere c) Find the capacitance

          Q. A spherical capacitor of inner radius $R_1$ and outer
radius $R_2$ is filled with an inhomogeneous dielectric
having $\epsilon = \epsilon_0 R$, where $\epsilon_0$ is the permittivity of the
vacuum and R is radial distance. Assume that $V = V_0$
on the inner sphere and $V = 0$ on the outer sphere.
a) By using Laplace equation find $\vec{D}$ and $\vec{E}$.
b) Find $\rho_s$ on the inner sphere
c) Find the capacitance

Q. A spherical capacitor of inner radius R1 and outer
radius R2 is filled with an inhomogeneous dielectric
having ϵ = ϵ0 R, where ϵ0 is the permittivity of the
vacuum and R is radial distance. Assume that V = V0
on the inner sphere and V = 0 on the outer sphere.
a) By using Laplace equation find D⃗ and E⃗.
b) Find on the inner sphere
c) Find the capacitance

Added by Michelle M.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Gokul R Nair

Step 1

Laplace's equation is given by: ∇^2V = 0 In spherical coordinates, Laplace's equation becomes: 1/r^2 ∂/∂r (r^2 ∂V/∂r) + 1/r^2 sinθ ∂/∂θ (sinθ ∂V/∂θ) + 1/r^2 sin^2θ ∂^2V/∂φ^2 = 0 Since the problem is spherically symmetric, we can assume that V depends only on Show more…

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solution needed as soon as possible please Q.A spherical capacitor of inner radius R and outer radius R is filled with an inhomogeneous dielectric having=Rwhere is the permittivity of the vacuum and R is radial distance.Assume that V=V on the inner sphere and V=0 on the outer sphere. a By using Laplace equation find D and E bFind p,on the inner sphere cFind the capacitance