3
votes
2answers
377 views

Potential of arbitrary charge distribution

Imagine this: You have a sphere of air where you have no charge and around this sphere you have a charge distribution $\rho(r,\theta,\phi)$. (For instance, this could be ...
1
vote
1answer
1k views

How to find electric scalar potential of infinite wire with Poisson/Laplace equation?

I though it will be easier then calculating the electric field and then integrating, but I am stuck. lets say we have an infinite wire, charged $\lambda$ per unit of length and its located at the ...
1
vote
2answers
635 views

Find the quantity of charge - given potential function

A potential function is given by $V(r)=\frac{Ae^{-\lambda r}}{r}$ Find charge density and hence charge. I first took the gradient of potential to get $\vec{E}(r)=\frac{Ae^{-\lambda ...
2
votes
2answers
786 views

Electric potential of sphere

(a) I am a little confused about this part. The point at A to B isn't radial. The electric field is radially outward, but if I look at the integral $$\int_{a}^{b}\mathbf{E}\cdot d\mathbf{s} = ...
4
votes
4answers
4k views

Infinitely charged wire and Differential form of Gauss' Law

I have tried calculating the potential of a charged wire the direct way. If lambda is the charge density of the wire, then I get $$\phi(r) = \frac{\lambda}{4 \pi \epsilon_0 r} \int_{-\infty}^\infty ...