Consider a conducting hollow sphere with radius R that is placed in a homogeneous electric field...

Consider a conducting hollow sphere with radius R that is placed in a homogeneous electric field E_0 = E_0 e_z

a) Calculate the electrostatic potential φ_0(r) for the homogeneous electric field E_0= E_0 e_z only and write the result in spherical coordinates.

b) Assume that the sphere is grounded i.e. put the potential φ(R)=0 and calculate the electrostatic potential φ(r)=0 inside and outside the sphere.

Hint: Consider that the electrostatic potential far away from the sphere should just give rise to the homogeneous electric field E_0, i.e. potential should have this limit at large distances.

c) Determine the surface charge density ρ(θ,φ) on the sphere.

Hint: The solution has the form ρ(θ,φ)& ρ’(cos(θ)).

d) Calculate the dipole moment p=∫r φ(r) dV of the induced charge density on the surface of the sphere where φ(r) ist the charge density.

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Expert Solution

Solving Laplace equation

a) and b)

image method

genius_generous answered 1 year ago

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