# Potential Difference and Potential Near a Charged Sheet

 P: 29 1. The problem statement, all variables and given/known data Let $${\rm A} = \left(x_1,y_1 \right)$$ and $${\rm B} = \left( x_2,y_2 \right)$$ be two points near and on the same side of a charged sheet with surface charge density $$+ \sigma$$ . The electric field $$\vec{E}$$ due to such a charged sheet has magnitude $$E = \frac {\sigma}{2 \epsilon_0}$$ everywhere, and the field points away from the sheet, as shown in the diagram. View Figure Part A What is the potential difference $$V_{\rm AB} = V_{\rm A} - V_{\rm B}$$ between points A and B? Part B If the potential at $$y = \pm \infty$$ is taken to be zero, what is the value of the potential at a point $$V_A$$ at some positive distance $$y_1$$ from the surface of the sheet? choices are: 1. infinity 2. negative infinity 3. 0 4. -E * y_1 2. Relevant equations $$\int_{\rm B}^{\rm A} \vec{C} \cdot d\vec{\ell} = \int_{x_2}^{x_1} C_x\,dx + \int_{y_2}^{y_1} C_y\,dy = C_x (x_1 - x_2) + C_y(y_1 - y_2)$$ $$V_{\rm AB}= -\int _B^A \vec{E}\cdot d\vec{l}$$ 3. The attempt at a solution Part A. $$V_{\rm AB} = V_{\rm A} - V_{\rm B}= \left(-E\right)\left(y_{1}-y_{2}\right)$$ Part B. I figure I'd use the equation I got in part A and set the bottom of the E field at y=0. In which case V = -E (y_1 - infinity) = infinity am i on the right track?