P (0, yp) q2 (X2, V2) 91 (0, y,) not to scale • The vector E, means the electric field at P due only to q- • The vector E, means the electric field at P due only to q2. • The vector E means the total electric field at P due to all charges. Item Charge (C) (x,y) m P None ( 0.00 , 5.44) q1 -8.87e-06 (0.00,-2.49 ) q2 3.87e-06 (1.91, 2.32 ) Determine the distance from q, to P: r, - 7.93 Determine the distance from q, to P: r, - 3.658 Determine the magnitude of E1. |EI = 1269.4621 Determine the magnitude of E2. |E = 2602.9514 Fill in the following table with all the appropriate components: Item x-component (N/C) y-component (N/C) -2.49 E2 1.91 2.32 Etot NOTE: • Green check only means "close enough". It does not mean perfect.

48. •• CALC A plastic rod with linear charge density A is bent into the quarter circle shown in Figure P23.48º. We want to find the electric field at the origin. Figure P23.48 a. Write expressions for the x- and y-components of the electric field at the origin due to a small piece of charge at angle 0. b. Write, but do not evaluate, definite integrals for the x- and y-components of the net electric field at the origin. c. Evaluate the integrals and write E in component form. net

Review Constants A point charge qi axis at z = 220 m, and a second point charge q2 -5.95 nC is on the y-axis at y = 1.20 m 4.45 nC is located on the x- Part A What is the total electric flux due to these two point charges through a spherical surface centered at the origin and with radius ri = 0 540 m ? ΑΣφ N-m2/C Submit Request Answer Part B What is the total electric flux due to these two point charges through a spherical surface centered at the origin and with radius r2 = 1.65 m ? ? N- m²/C Submit Request Answer Part C What is the total electric flux due to these two point charges through a spherical surface centered at the origin and with radius r3 = 2.50 m ? ΑΣφ N. m2/C Submit Request Answer Next> Provide Feedback

2- Suppose a point charge q is placed at the center of a neutral (initially uncharged) thick spherical conducting shell of inner and outer radii = a and b respectively as shown in the figure, a) How much induced charge will accumulate on the inner surface of the conducting shell? b) How much induced charge will accumulate on the outer surface of the conducting shell? c) Find expressions for the electric field E as function of r in the three regions r b. d) Prove that E satisfies the boundary conditions at the inner and outer surfaces of the thick spherical conducting shell. e) Find expressions for the electric potential V as function of r in the three regions r b.