Problem 1: Dielectric materials in capacitors A capacitor is constructed with an air gap of 2 mm between its parallel plates. A. What is the capacitance per square meter for such a capacitor? Use this result to calculate the capacitance if the plates have an area of 0.3 m2. +Q B. If the capacitor stores a charge of Q, determine an expression for the voltage difference between the plates and for the magnitude E0 of the electric eld between the plates. C. If you were to halve the separation between the plates, determine for each quantity listed if it increases or decreases and by which factor, or if it remains unchanged: 1. the capacitance of the capacitor, 2. the voltage difference between the plates, 3. the magnitude ED of the electric eld between the plates. The space between the plates is entirely lled with paper, which has a dielectric constant of K = 3.7. D. What is the capacitance per square meter for such a capacitor? Use this result to calculate the capacitance if the plates have an area of 0.3 m2. E. If the capacitor stores a charge of Q, determine an expression for the voltage difference between the plates and for the magnitude E K of the electric eld between the plates. F. If you were to halve the separation between the plates, determine for each quantity listed if it increases or decreases and by which factor, or if it remains unchanged: 1. the capacitance of the capacitor, 2. the voltage difference between the plates, 3. the magnitude Ex of the electric field between the plates. We now fill only half of the space between the plates with the paper, as pictured here. We can te paper -Q calculate the capacitance of this capacitor in a few ways. G. Imagine that we are storing still a charge of Q on the plates. 1. Use your result from C2 and F2 to determine an expression for the total potential difference between the plates. (Hint: What is the potential difference: (a) from the positive plate to the mid-point, (b) from the mid-point to the negative plate? 2. Use your previous result to calculate the capacitance of the capacitor. H. The capacitor is equivalent to two capacitors connected as paper +0 paper -Q pictured, where the mid-equipotential line has been replaced by conductors (also equipotential regions). Use your results from Cl and F1 to determine the capacitance of this combination