Electrostatic Potential - Electricity and Magnetism - Past Paper, Exams of Electromagnetism and Electromagnetic Fields Theory

Download Electrostatic Potential - Electricity and Magnetism - Past Paper and more Exams Electromagnetism and Electromagnetic Fields Theory in PDF only on Docsity! NIU Ph.D. candidacy examination Fall 2009 (9/19/2009) Electricity and Magnetism Solve 3 out of 4 problems. Problem 1: Electrostatic potential [40 points] Consider an electrostatic potential φ r( ) = Ae −κ r r : a) Using the Poisson equation, find the charge density distribution in the space except at the origin. (15 points) b) The fact that the potential becomes infinity at the origin means the existence of a point charge at the origin. First obtain the electric field from the potential φ r( ) , then find the magnitude of the point charge and its sign. (15 points) c) Find the total charge distributed other than the origin, also indicate its sign. (10 points) Problem 2: A uniformly polarized ferroelectric slab is inserted into a parallel plate capacitor [40 points] A uniformly polarized ferroelectric slab is inserted into a parallel plate capacitor as shown in the Figure. The capacitor area is A, and the lateral sizes are much larger than a, b. The two plates of the capacitor are connected through a thin wire. a) Neglecting edge effects, determine the electric field everywhere in the capacitor. [16 points] b) What is the electric field inside the ferroelectric plate for b >> a, and for vanishing b? [8 points] c) Determine the force vector acting on the upper capacitor plate. [16 points] Figure 1