$(13\%)$ Problem $3$: A neuron is a body cell that functions to create and transmit electrical signals. To do this, it uses chemical processes to maintain an electrical potential difference across its cell membrane. In this problem we will use our knowledge of electrical relationships to estimate the amount of charge on the membrane. Neurons come in a range of sizes, but a typical one may have a cell body of $20m(2{10}^{-5}(m))$ across. The thickness of the membrane is the same for most neurons $-$ about $5nm(5{10}^{-9}(m)).$ The potential difference across a resting nerve membrane is about $70mV(70{10}^{-3}(V)).$ We'll model a plece of the cell membrane $10m10m$ across as a pair of infinite parallel plates separated by a distance $d=5nm,$ with one plate representing the inner edge of the membrane and the other representing the outer edge of the membrane.

$25\%$ Part $($a$)$ Assuming the space separating the two plates of our membrane is empty space, calculate the electric field between the plates in V$/$m$.$