Problem #3: Common "coaxial" cables have a central conductor (the core), separated by a dielectric insulator from an outer shield conductor (usually braided wire). See figure. plastic jacket dielectric insulator metallic shield Assume the radius of the central core conductor is "a", the outer radius of the dielectric insulator is "b", and the outer radius of the metallic shield is "c". Assume the length of the cable is L, which is much bigger than c. Obviously, c >b >a. The dielectric constant of the insulator is K. The length of the entire cable is "L". centre core Since this is a two-conductor object, the entire wire has a capacitance! Show a derivation of the capacitance of this wire in terms of given parameters and known constants. (This is a multi-step problem.). If there is an integral you can't do (or don't have time to do), you can leave it in integral form, but make sure the integral is specified sufficiently for a math expert with no knowledge of physics to solve. Problem #4: Five objects, each with a known charge, are arranged as follows. The object in the middle, object "A", has a charge of -1µC and a mass of 2.0 grams. Object "A" is exactly 10cm away from three of the other objects, and 20cm away from the fourth object. 0.4mC 20cm -0.4mC A 10cm 0.8mC 10cm 10cm 0.2mC a) Calculate the magnitude of the force experienced by particle "A". Be sure to give the correct units for your answer. b) In what direction will this force point? (Indicate how this angle is defined in your solution.) c) What is the electrical potential energy of charge A? (not the whole system). This can be answered independently of parts a and b.

Problem #3: Common "coaxial" cables have a central conductor (the core), separated by a dielectric insulator from an outer shield conductor (usually braided wire). See figure. plastic jacket dielectric insulator metallic shield Assume the radius of the central core conductor is "a", the outer radius of the dielectric insulator is "b", and the outer radius of the metallic shield is "c". Assume the length of the cable is L, which is much bigger than c. Obviously, c >b >a. The dielectric constant of the insulator is K. The length of the entire cable is "L". centre core Since this is a two-conductor object, the entire wire has a capacitance! Show a derivation of the capacitance of this wire in terms of given parameters and known constants. (This is a multi-step problem.). If there is an integral you can't do (or don't have time to do), you can leave it in integral form, but make sure the integral is specified sufficiently for a math expert with no knowledge of physics to solve. Problem #4: Five objects, each with a known charge, are arranged as follows. The object in the middle, object "A", has a charge of -1µC and a mass of 2.0 grams. Object "A" is exactly 10cm away from three of the other objects, and 20cm away from the fourth object. 0.4mC 20cm -0.4mC A 10cm 0.8mC 10cm 10cm 0.2mC a) Calculate the magnitude of the force experienced by particle "A". Be sure to give the correct units for your answer. b) In what direction will this force point? (Indicate how this angle is defined in your solution.) c) What is the electrical potential energy of charge A? (not the whole system). This can be answered independently of parts a and b.