Students are doing experiments involving the electrical charging of objects. They have a charged conducting disk that is fixed on an insulating rod, as shown, and want to determine the sign of the charge on the disk. They also have the following equipment. Several identical plastic spheres that are each attached to an insulating string A cloth that can be used to give the spheres a positive charge A cloth that can be used to give the spheres a negative charge A grounding wire (a) Describe a procedure the students could use to determine the sign of the charge on the disk, including the measurements to be taken or observations to be made. Please respond on separate paper, following directions from your teacher. Disk 1 Disk 2 Note: Figure not drawn to scale. The students now want to determine whether the same amount of negative charge is deposited on a disk each time it is rubbed with a cloth. They place disk 1 with charge 1 on a rough, horizontal, insulating surface. They take disk 2 and carefully rub it with the same motion each time. They carefully bring disk 2 near disk 1, as shown, until disk 1 begins to slide, and measure the distance d between the disks at which the disk 1 starts to slide. They discharge disk 2 and repeat the process, each time counting the number of times they rub sphere 2. (b) Let 92 be the net charge deposited on disk 2 as a result of rubbing the disk once, and Ff be the magnitude of the maximum force of static friction on the disk. Derive an expression relating d to 92 that can be applied to any trial, including other given quantities and physical constants, as appropriate. Assume that d is much larger than the dimensions of the disks, and that the disks can be treated as point charges. O Please respond on separate paper, following directions from your teacher. (c) The students are to create a graph from the experimental data that can be used to determine whether the same amount of charge is deposited on disk 2 each time it is rubbed. i. Based on the equation in part (b), state what quantity should be plotted on the horizontal axis and what quantity should be plotted on the vertical axis to produce a useful graph. Horizontal axis: Vertical axis: Conducting Disk Insulating Rod Stand