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.

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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.

•% Two charges, qa and q are located at the center of spherical cavities of radius a and b within a conducting sphere of radius R. Find the charge densities a, b, and R. Find Ē (r>R). Find Ewithin each cavity. What are the forces on qe and qb? 2°

Q4/ The direction of electric field due +0 positive charge is: O(a) away from the charge (b) Towards the charge (c) Both (a) and (b) (d) None of the above

•24 Figure 23-40 shows a section of a long, thin-walled metal tube of radius R = 3.00 cm, with a charge per unit length of A = 2.00 × 10-8 C/m. What is the magnitude E of the electric field at radial distance (a) r= R/2.00 and (b) r= 2.00R? (c) Graph E versus r for the range r = 0 to 2.00R. R. Figure 23-40 Problem 24.

5. Point charge q₁ = -5nC is at the origin and point charge is q₂ = +3nC on the -axis at x=3.00cm Point P is on the y -axis at at y=4.00cm (a) Calculate the electric fields and E2 at point Pdue to the charges qi and 92. Express your results in terms of unit vectors ((b) Use the results of part (a) to obtain the resultant field at P expressed in unit vector form.

•29 Figure 22-47a shows a nonconducting rod with a uniformly dis- tributed charge +Q. The rod forms a half-circle with radius R and produces an electric field of magnitude Eare at its center of curvature P. If the arc is collapsed to a point at distance R from P (Fig. 22-47b), by what factor is the magnitude of the electric field at P multiplied? +Q +Q P R (a) (b) Fig. 22-47 Problem 29.