Question

1. For the point charge and grounded conducting sphere (method of images solution), using the following potential calculate \begin{equation} V(r, \theta) = kq \left[ \frac{1}{\sqrt{r^2 + d^2 + 2rd \cos \theta}} - \frac{a}{d \sqrt{r^2 + b^2 + 2rb \cos \theta}} \right] \end{equation} (a) The electric field components, $E_r$ and $E_\theta$ using $\vec{E} = -\nabla V$. (b) The charge distribution on the surface of the sphere (set $r = a$) using $\begin{equation} E_{normal} = E_r = \frac{\sigma}{\epsilon_0} \end{equation}$ (c) The total charge on the sphere using $\begin{equation} Q_{induced} = \int_S \sigma da \end{equation}$

          1. For the point charge and grounded conducting sphere (method of images solution), using the following potential calculate
\begin{equation} V(r, \theta) = kq \left[ \frac{1}{\sqrt{r^2 + d^2 + 2rd \cos \theta}} - \frac{a}{d \sqrt{r^2 + b^2 + 2rb \cos \theta}} \right] \end{equation}
(a) The electric field components, $E_r$ and $E_\theta$ using $\vec{E} = -\nabla V$.
(b) The charge distribution on the surface of the sphere (set $r = a$) using
$\begin{equation} E_{normal} = E_r = \frac{\sigma}{\epsilon_0} \end{equation}$
(c) The total charge on the sphere using
$\begin{equation} Q_{induced} = \int_S \sigma da \end{equation}$

1. For the point charge and grounded conducting sphere (method of images solution), using the following potential calculate

V(r, θ) = kq [ (1)/(√(r^2 + d^2 + 2rd cosθ)) - (a)/(d √(r^2 + b^2 + 2rb cosθ))]

(a) The electric field components, Er and Eθ using E⃗ = -∇ V.
(b) The charge distribution on the surface of the sphere (set r = a) using
Enormal = Er = (σ)/(ϵ0)
(c) The total charge on the sphere using
Qinduced = σ da

Added by James N.

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