Conductor problem in which the conductor consists of two parallel plates

[Benzoate]

Yes, you now have an ODE for V(x) involving only V(x), its derivatives, and some constants; so there is your answer to part (d). For part (e) you are asked to solve this ODE for V(x), to make it easier to work with I recommend you collect all your constants into one, say,

$$\kappa \equiv \frac{-I}{\epsilon_0 A} \sqrt{\frac{m}{2q}}$$

$$\Rightarrow \frac{d^2V}{dx^2}= \kappa V^{-1/2}$$

Now, try to solve this ODE.

my only variable is V since V is a function of x . I am solving an equation for V(x). So my only problem with e is just the math since I am only rearranging all the constants to one side of the equation and V by itself on the other side of the equation .

 

[gabbagabbahey]

Hint:

$$\frac{d^2V}{dx^2}= \frac{d}{dx} \left( \frac{dV}{dx} \right)$$

Rewrite
$$\frac{dV}{dx}$$

as $V'$ and multiply both sides of the equation by $V'dx$ then integrate from x=0 to x=d.