You have the electric potential function, $V(x,y,z)=$Axyz$+B{y}^2+C{z}^2,$ where $A=4\frac{V}{m^3},B=3\frac{V}{m^2},$ and $C=-5\frac{V}{m^2}.$ Find $E_z$ at the point: $(2m,9\mathrm{.}2m,2m).$

Answer in units of $\frac{V}{m}.$

$-20\mathrm{.}8$

$0$

$-52$

$-53\mathrm{.}6$

$-57\mathrm{.}6$

$-47\mathrm{.}2$

$-50\mathrm{.}4$

$-2\mathrm{.}4$

$-49\mathrm{.}6$

$-52\mathrm{.}8$

A long cylindrical shell has a uniform current density. The total current flowing through the shell is $10$ A $.$

The permeability of free space is $1\mathrm{.}25664{10}^{-6}T*\frac{m}{A}.$

Find the magnitude of the magnetic field at a point $r_1=6\mathrm{.}8cm$ from the cylindrical axis and far from either end of the cylindrical shell.

Answer in units of mT$.$

$0\mathrm{.}0322581$

$0\mathrm{.}0266667$

$0\mathrm{.}0411765$

$0\mathrm{.}0451613$

$0\mathrm{.}0509091$

$0\mathrm{.}0491803$

$0\mathrm{.}0426667$

$0\mathrm{.}0314286$

$0\mathrm{.}0294118$

$0\mathrm{.}0363636$