A square loop has a charge density λ = |x| at y = ±a and |x|
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- O [HW3.1] A solid metal ball (radius a) is grounded inside a floating (isolated) metal sphere (inner radius b, outer radius d). The sphere comes with total charge Q. Find surface charge density on every surface (the outer surface of the metal ball, inner and outer surface of the sphere), and capacitance of the system.For a uniformly charged conductor, E = 0 inside the conductor O V = 0 inside the conductor V = 0 everywhere O E = 0 everywhereThe potential distribution in a dielectric material (& = 8) is V = 4x³yz² V. Find V, E, and P at point (2, –5, 3).
- An uncharged, infinitely long conducting cylinder of radius a is placed in an initially uniform clectric ficld E = Eoi, such that the cylinder's axis lics along the z axis. The resulting clectrostatic potential is V (x, y, z) = Vo for points inside the cylinder, and Ega?x x² + y? V (r, y, z) = Vo – Egx + for points outside the cylinder, where Vo is the (constant) clectrostatic potential on the conductor. Usc this expression to determine the resulting clectric ficld, E.Consider two long, parallel, and oppositely charged wires with linear charge density +λ and -λ of radius r with their centers separated by a distance D (? ≫ ?). Show that the capacitance per unit length of this pair of wires is given by the following, and show the work required to set up an integral for E, ∆? and then finding C.Two circular disks spaced 0.50 mm apart form a parallel- plate capacitor. Transferring 3.00×109 electrons from one disk to the other causes the electric field strength to be 1.00×105 N/C. [ What are the diameters of the disks?