Question Two small insulating spheres with radius 6.50×10−2 m are separated by a large center-to-center distance of 0.600 m . One sphere is negatively charged, with net charge -2.40 μC , and the other sphere is positively charged, with net charge 3.95 μC . The charge is uniformly distributed within the volume of each sphere. a.What is the magnitude E of the electric field midway between the spheres?Take the permittivity of free space to be ϵ0 = 8.85×10−12 C2/(N⋅m2) .

1. (10 points.) Write an expression for the energy balance of the surface in terms of T, T. Fc and the other given parameters. Keep your expression algebraic, using the notation given above. 2. (10 points. Write an expression for the energy balance of the atmospheric layer in terms of T., TA. Fc and the other given parameters. Keep your expression algebraic. 3. (10 points.) Combine your answers from questions 1 and 2 to eliminate Fc. Write new expression below. Keep your expression algebraic, and simplify your expression as much as possible your 4. (10 points. Use equation (1) to eliminate T, from the expression you obtained in question 3. Write your new expression below, and keep your expression algebraic.

2. Assassination is a type of covert action. Do you think assassination is an acceptable action or is an action that should be forbidden, never done? Explain your answer.

v MI 7. Let (r) = for r e A := (0,0) (i) Find the pointwise limit f off (ii) Show that each f, is bounded on A but the pointwise limit f of the sequence is not bounded on A. (ii) Decide whether or not the convergence in () is uniform, prove your claim. (iv) use the e-strip to prove your claim in (iii).

A solid disk, a hoop, and a solid sphere are released at the same time at the top of an inclined ramp. Each has mass M and radius R. They all roll without slipping. In what order (fastest to slowest) do they reach the bottom of the ramp, if the moments of inertia of the disk, hoop, and sphere are ½ MR2, MR2, and 2/5 MR2? A) disk, hoop, sphere B) disk, sphere, hoop C) sphere, hoop, disk D) hoop, sphere, disk E) sphere, disk, hoop

R W R3 ww 10 12 ww R2 1 Write down the Kirchhoff Junction equation and solve it for I; in terms of 12 and 13. Write the result here: Ij = write down the Kirchhoff Loop equation for a loop that starts at the lower left corner and follows the perimeter of the circuit diagram clockwise. 0 write down the Kirchhoff Loop equation for a loop that starts at the lower left corner and touches the components 10V, Ry, 4V, and Ry O The resistors in the circuit have the following values . - R2 • Ry=60 Ry=130 Solve for all the following (some answers may be negative); 11 - Amperes 12 Amperes 13 Amperes NOTE: Forthin

3. Find the area between the curve y = 2^x andthe chord joining the points (0,1) and (2,4). 4. Find the coordinates of the centroid bounded bythe curve y = x^3 and the line x = 2.