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Name(Last, First):______________________________,___________________ RuID#:__ __ __ __ __ __ __ __ __ 1. In the Bohr theory of the hydrogen atom, an electron moves in a circular orbit about a proton. The radius of the orbit is 0.53 x 10-10 m. a) Find the electric force between the two. b) Assuming that only this force is present, what is the speed of the electron? 2. A) Determine the electric potential at point P for a ring of radius R that has a uniformly distributed charge Q. B) Determine the electric field at point P. 3. An insulating solid sphere of radius “a” has a uniform volume charge density ρ and carries a total charge Q. A) Calculate the magnitude of the electric field at a point outside the sphere (r > a). B) Find the magnitude of the electric field at appoint inside the sphere (r < a). 4. Two charges are fixed at the positions shown. The distances a and b are known. The charge at the origin is negative, -q1. The charge q2 at (x,y)=(a,b) is positive. Find the force that would be exerted on a charge q 3 if it were placed at an arbitrary point x,y. 5. A charge Q is uniformly distributed along a semicircle of radius R whose center is a distance “a” from the origin. What point charge would have to be placed at the origin so that the electric field at the center of the semi-circle would be zero? 6. A solid copper sphere has been given a charge Q. The sphere has a radius R. The electric field is measured and found to be zero inside the sphere (conducting sphere) and given by |𝐸⃑ | = 𝑘𝑄/𝑟 2 outside of the sphere (r is the distance from the center of the sphere, the direction of 𝐸⃑ is radially out). Find the difference in the electric potential between a point a distance 3R from the center of the sphere and a point at the center. 7. Consider a cubical surface of side L. The bottom is in line with the x,z plane and the back corner is at x=B. There is an electric field present given by: 𝐸⃑ = 𝐴𝑥𝑖̂ + 𝐵𝑦 2 𝑗̂ + 𝐶𝑥𝑘̂ (A, B, C are known constants. a) Find the electric flux through the front y-z surface (horizontal dotted lines). b) Find the electric flux through the front x-z plane (vertical dotted lines).