Figure 1.52 shows a spherical shell of charge, of radius a and surface density σ, from which a small circular piece of radius b << a has been removed. What is the direction and magnitude of the field at the midpoint of the aperture? Solve this exercise in three ways: a) direct integration, b) by superposition, and c) using the relationship for a force on a small patch.

A cylinder of radius R has a charge density given by p = Po/r where po is a constant, for r R. Find the electric field both inside and outside the cylinder using Gauss' law. 1.

Consider an infinitely long cylinder with radius R. The cylinder is an insulator and it is positively charged, the charge per unit of length is A. (Hint: because it is an insulator you should assume that the charge is spread uniformly across its entire volume). By reflecting on the symmetry of the charge distribution of the system, determine what a) the E-field lines look like around the cylinder. Describe the E-field in words and with a simple sketch. In order to give a complete description of the E-field lines make two sketches: i) one with a side view of the cylinder, ii) one with a cross-sectional view of the cylinder. Make sure to also show the direction of the E-field lines. b) (-- . the figure. Your goal for this part is to properly use Gauss' law to calculate the electric field at point P. Follow the 5 steps below. Consider a point P outside the cylinder, at a distance d from its axis, d > R, as shown in

A thin plastic rod of length L has a positive charge Q uniformly distributed along its length. We willcalculate the exact field due to the rod in the next homework set. In this set, we will approximatethe rod as several point sources and develop the Riemann sum as an intermediate step on the wayto writing an integral.For those aiming at a P rating, you may use L = 3.0m , Q = 17 mC, and y = 0.11m to calculate theanswer numerically first and substitute variables for them only as required in the problem statement.For those aiming at an E rating, leave L, Q and y as variables. Substitute numbers only whererequired in the problem statement, and only as a last step

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Solve 4,5