. In the study of electricity and magnetism Ampre's law was originally given by: V X g = \"of Where E is the magnetic eld, no is the magnetic constant, and f is the current densityl. We will use some facts about basic circuits and Stoke's Theorem to show that this form of Ampre's law is false. A capacitor is two metal plates separated by a material that prevents charge from moving through. Let's say that we have a capacitor in R3 set up with two circular disks with radii of 1 meter the lower one centered on the point (0, 0, 1) the upper one centered at (0,0, 2) (both disks are parallel to the cry-plane). Suppose that we have a wire moving down from the lower disk and a wire and a wire moving up from the upper disk. Suppose that at time to there is a current Io > 0 moving through both wires. Notice that at this time there is no current passing between the disks. Here is a simplied diagram: 1Current density is dened so that ff j- Vida is equal to the current passing through the surface S. S . To Pass this question you must: (a) Describe two surfaces 51 and $2 with boundary C, so that you can apply Ampre's law to show that ff V x E - da and V x E - da have different values 31 S2 (b) Then use Stoke's Theorem to show that both of the surface integrals have the same value. (c) Conclude that Ampre's law is incorrect. ) ) (d Show all important steps in preforming these calculations. (e Present your work in a coherent manner