13) a) A ring of charge sits in the xy plane. It has a radius of 0.25 m and a linear charge density of A=0.2C/m. What is the electric potential at a point z directly above its center? b) What is the magnitude and direction of the electric field at that point where you computed the potential?

B5

Problem 5 Consider a parallel-plate capacitor with a plate area of A = 8.50 cm². The separation between the plates is d₂ = 3.00 mm (the space between the plates is filled with air). The plates of the capacitor are charged by a 6.00 V battery, i.e., the potential difference between the plates is V₂ = 6.00 V. The plates are then disconnected from the battery and pulled apart (without discharge) to a sepa- ration of df = 8.00 mm. In the following, neglecting any fringing effects. (a) Will the new potential difference between the plates be larger, smaller, or the same compared to the initial potential difference of V₂ = 6.00 V? Explain. (Hint: Note that the charge will not change when the plates are pulled apart. Why is that?) (b) Find the potential difference Vf between the plates after the plates have been pulled to their new, larger separation df. (c) Find the electrostatic energy stored in the capacitor before and after the plates are pulled apart. (d) To separate the plates, you will…

If you already know the electric field, you can find the change in electrostatic potential between two points A and B by integrating the field along an arbitrary path joining these two points, VB - VA = while the field at r > R is == E(r) = 1 Recall from Gauss's law that the magnitude of the electric field E(r) at a radial distance r ≤R from the center of a uniformly charged sphere with total charge Q and radius R is given by E(r) = B Ē. ds. 1 Q 4π€0 R3¹ 1 Q p2 4πεο If the charge Q is positive, the field points radially out. We will now analyze the electric potential due to a uniform spherical charge distribution.