1. Suppose we were to treat the Earth as a big spherical conductor. Suppose also that the Earth has a net positive charge such that a proton just above the Earth's surface has zero net force on it. (It has zero net force because the gravitational and electric forces on it cancel.) What would the net charge of the Earth be in this case? Look up any constants that you need. 2. Two parallel innite sheets of charge are placed a distance (1 from each other. The left sheet is at :1:: : 0 (parallel to the y: -plane) and right sheet Is at :11: L. The net electric eld at :11: :73L is E: +41 NE C. The net electric eld at :11: LE '.3is E: +61 N EC. Determine the surface charge densities UL and 0'11: on the left and right plates, respectively. (Be careful with signs and directions of electric eld in your setup of the problem because it's easy to get them wrong. I highly suggest you check your answer by making sure you get the correct E-eld at the end.) . Consider an imaginary cube centered at the origin with side length (11.. This means that one corner, for example, is at (:1:3 y? z : (\"E-"lg: _'1-..-"l2: 1.1.J,:-"'2) and the opposite corner is at (137': y} a) : (11112413121112) In the region occupied by the imaginary cube, the electric eld is given by E : EU cos(:21er.- (1)11. where E0 is a positive constant with appropriate dimensions. What is the net charge enclosed by the imaginary cube? (Hint: | suggest you fully understand the similar WileyPLUS problem before doing this one.)