Practice test 2, hints Question 1: Magnetic field lines always form closed loops. Question 2: Coulomb’s law: . Question 3: The potential outside a conducting charged sphere is equal to that of a point charge with the same charge. It increases as we get closer to the surface. The potential inside the sphere and on the surface is the same everywhere, since the sphere is a conductor. So any place on the sphere has the highest potential. Question 4: Electric flux = E*A cosθ. Here cosθ = 1. Question 5: U = kq1q2/d If you use SI units consistently, the answer will come out in SI units. Question 6: I = Q/t = (5 C)/(2 s) Question 7: The proton has charge e and the neutron has charge 0. Question 8: Bbefore = μ0nI, Bafter = μ0n2I = 2 Bbefore The ONLY things that matter are n = number of turns per length and I = current. Question 9: The proton and the positron have the same charge and they are in the same field, so they experience the same force, F = qE. The acceleration is a = F/m, so the lighter particle (the positron) has the greater acceleration. When the particles reach the other plate, the potential energy U = qV has been converted into kinetic energy ½ mv2. Both have the same kinetic energy (energy conservation). Question 10: the bottom two resistors in series: (1.5 + 2.5) kΩ = 4 kΩ the two branches in parallel: ¼ + ¼ = 1/Rp, Rp = 2 kΩ Rp in series with 1.5 kΩ: R = 3.5 kΩ Power P = V2/R Question 11: E is the gradient of the potential V. The spacing between the equipotential lines near point A is ∆V = 0.4 V. The spacing between the lines is ∆r = 2 m. |E| = ∆V/∆r. Question 12: Consider a charged particle with mass m and charge q which at t = 0 has a velocity v perpendicular to B. This particle experiences a force with magnitude F = qvB perpendicular to its velocity. A force perpendicular to the velocity results in centripetal acceleration a = F/m = v2/r. The particle will move along a circular path. The radius of the circle is r = mv2/F = mv2/(qvB) = mv/(qB), Here m, q, v, and r are given, solve for B. Be sure to use SI units consistently. Question 13: P = IV, V = IR, therefore P = I2R. Question 14: The energy stored in a capacitor: U = (1/2)CV2. Question 15: The electric field is minus the gradient of the potential V. If E is constant and nonzero, the gradient of V cannot be zero, the potential cannot be zero everywhere, and the potential cannot be constant.