Find E_r & E_θ for Grounded Conducting Sphere in Uniform Electric Field

[nmsurobert]

Homework Statement

Grounded conducting sphere in uniform electric field has potential
V(r,θ) = -V_o(1 - (R/r)³)*cosθ

Find E_r and E_θ.

Homework Equations

The Attempt at a Solution

In the textbook I found
E_r = -∂V/∂r

E_θ = -1/r ∂V/∂θ

Those are in the chapter we're working with but those two equations are in the section talking about the electric field of dipoles. Do those equations apply for the problem I'm working on?

 

[Simon Bridge]

By definition: $\vec E = -\vec\nabla V$ ... you will need $\nabla$ in spherical-polar coordinates.

Check how the equations in your book were derived - make sure you understand the reasoning involved. Then you can make a determination about how appropriate they are for your situation.

 

[nmsurobert]

By definition: $\vec E = -\vec\nabla V$ ... you will need $\nabla$ in spherical-polar coordinates.

Check how the equations in your book were derived - make sure you understand the reasoning involved. Then you can make a determination about how appropriate they are for your situation.

the front of the book has a legend for the gradient in spherical coordinates so i used that. the question was just worded weird.

also, the question asks for "surface charge distribution of the sphere".
is that just the surface charge density?

σ = q/A?

 

[nmsurobert]

or ρ = ∈_o∇E

 

[Simon Bridge]

the front of the book has a legend for the gradient in spherical coordinates so i used that. the question was just worded weird.

Then you have the answer to your first question - well done.

also, the question asks for "surface charge distribution of the sphere".
is that just the surface charge density?

This is another odd wording I think. You seem quite good at figuring this stuff out...
How would you normally express a charge distribution?

 

[nmsurobert]

The word "distribution" is what's throwing me off but if this were an exam I'd say it's asking for area charge density. That's how the charge is distributed over the surface per unit area.