U2-EC00A. Determine the X- and Y-Components of the Electric Field at Point P in the Situation

Physics 112 HW4

Due Wednesday 8 February 2017

U2-EC00. In class we did a few examples with numbers. Now, repeat them using symbols! Determine the x- and y-components of the electric field at the points indicated (P) in the three situations below. In all cases, a charge +Q is spread evenly over a thin rod of length L. Your expressions will be in terms of Q, x, L, and fundamental constants (e.g., ‘k’). You may leave your answers in the form of definite integrals without evaluating them, but isn’t it more fun to actually do the integrals?

U2-EC00A. Determine the x- and y-components of the electric field at point P in the situation at right. Note the point P is halfway between the two oppositely charged thin rods (charge spread out evenly). Your expression will be in terms of Q, L, d, and fundamental constants. NOTE: It is possible to do this quickly and easily using symmetry and the result from a previous problem.

U2-EC01. An thin wire with charge +Q spread evenly over its length is bent into a circular arc that subtends an angle 2θo as shown at right. Derive an expression for the electric field at the center of the circle that would form if the arc went all the way around. Your expression will be in terms of Q, R (the radius of the arc), θo, and fundamental constants.

U2-EC04. Consider the charge distribution at right. A long thin insulator is bent into a semicircle with radius R. A charge +Q is evenly distributed on the top half, while a charge –Q is evenly distributed on the bottom half. Derive an expression for the magnitude and direction of the electric field at point P in the middle of the semicircle.

U2-EC05. An infinitely long, thin insulating rod lies on the x-axis. For x<0, the rod has a uniform linear charge density of –λ. For x>0, the rod has a uniform linear charge density of +λ. Derive an expression for the magnitude and direction of the electric field at points on the y axis (in terms of y, , and fundamental constants). You may, if you wish, leave your answer in the form of an integral.

U2-EC03. (Wolfson, Ch. 20 Problem 75) A thin rod extends along the x axis from x = 0 to x = L and carries a linear charge density λ = λo(x/L)2, where λo is a constant. Derive an expression for the electric field at the position x = –L. You may leave your answer in the form of a definite integral.