Question

James stands next to the Van de Graaff generator and gets a shock as he holds his knuckle 0.2 m from the machine. In order for a spark to jump. The electric field strength must be 3 x 10 V/m. At this distance, what is the potential difference between James and the generator?

Answer 1

Let's assume the electric field strength $E = 30V/m$ to be uniform at the distance $\Delta x = 0.2m$. Then the potential difference $\Delta \varphi$ can be found from its definition:

$$E = -\dfrac{\Delta \varphi}{\Delta x}\\ \Delta \varphi = -E\Delta x\\ \Delta \varphi = -30V/m\cdot 0.2m = -30V$$

Answer. -30 V.