An infinite non-conducting sheet with a uniform surface charge density sets up parallel equipotential surfaces. Any pair of surfaces differing by $25.0 \mathrm{V}$ are separated by $8.80 \mathrm{mm}$. $\left(a\right)$ What is the magnitude of the surface charge density? $\left(b\right)$ If an electron is released near the sheet, does it tend to move from higher to lower potential or vice versa?

In figure $\left(\mathrm{a}\right)$, we move an electron from an infinite distance to a point at distance $R=8.00 \mathrm{cm}$ from a tiny charged ball. The move requires work $W=5.32\times {10}^{-13} \mathrm{J}$ by us. What is the charge $Q$ on the ball? In figure $\left(\mathrm{b}\right)$, the ball has been sliced up and the slices spread out so that an equal amount of charge is at the hour positions, on a circular clock face of radius $R=8.00 \mathrm{cm}$. Now the electron is brought from an infinite distance to the centre of the circle. With that addition of the electron to the system of $12$ charged particles, what is the change in the electric potential energy of the system?

$\left(\mathrm{a}\right) \left(\mathrm{b}\right)$

Two isolated, concentric conducting spherical shells have radii $R_1=0.500 \mathrm{m}$ and $R_2=1.00 \mathrm{m},$ uniform charges $q_1=+3.00 \mathrm{\mu C}$ and $q_2=+1.00 \mathrm{\mu C}$, and negligible thicknesses. What is the magnitude of the electric field $E$ at radial distance $\left(a\right)$ $r=4.00 \mathrm{m}$, $\left(b\right)$ $r=0.700 \mathrm{m}$ and $\left(c\right)$ $r=0.200 \mathrm{m}$? With $V=0$ at infinity, what is $V$ at $\left(d\right)$ $r=4.00 \mathrm{m}$, $\left(e\right)$ $r=1.00 \mathrm{m}$, $\left(f\right)$ $r=0.700 \mathrm{m}$, $\left(g\right)$ $r=0.500 \mathrm{m}$, $\left(h\right)$ $r=0.200 \mathrm{m}$ and $\left(i\right)$ $r=0$? $\left(j\right)$ Sketch $E\left(r\right)$ and $V\left(r\right)$.

Two metal spheres, each of radius $3.0 \mathrm{cm}$, have a centre-to-centre separation of $2.0 \mathrm{m}$. Sphere $1$has charge $+1.0\times {10}^{-8} \mathrm{C}$ and sphere $2$ has charge $-8.0\times {10}^{-8} \mathrm{C}$. Assume that the separation is large enough for us to say that the charge on each sphere is uniformly distributed (the spheres do not affect each other). With $V=0$ at infinity, calculate $\left(a\right)$ the potential at the point halfway between the centres and the potential on the surface of $\left(b\right)$ sphere $1$and $\left(c\right)$ sphere $2$.