The electrostatic potential V (x, y) in free space in a region where the charge density p is zero, is given by V(x, y) = 4e2x +f(x) – 3y² Given that the x-component of the electric field, Ex and V are zero at the origin f(x)is
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- The electric flux density of a charge distribution with spherical symmetry is given by (a³po -âr, r2 a 3r2 rpo D = r a C-A ring and a disk both are centered at (0, 6, 3) and are both lying on the plane y = 6. The ring has a radius of 7 m, while the disk has a radius of 9 m, so that the ring is around the disk. Determine the magnitude of the electric field in kV/m at point (0, -9, 3) if the ring has a total charge of -8 mC and the disk has a total charge of 6 mC. All coordinates are measured in meters.Ra1 +9 -9 Rea Consider two concentric spherical conductors, separated by an isolating material with (absolute) permittivity e. The two conductors have radius R1 and R2, they are put on a potential V and V2, which leads to a charge +q and –q sitting on them, respectively. By the problem's spherical symmetry, we see that the charge on each conductor is distributed uniformly, and that, in spherical coordinates, the electric field between the two conductors is of the form E(r) = -E(r) er. Determine the capacity C using the following steps: 1. Use Gauss's Law in integral form, with N a ball of radius r (R2 < r < R1), to find an expression for E(r) in terms of q. 2. Calculate AV = Vị – V2 using the formula - E•dr Δν and with C the black line segment indicated on the drawing (parallel with e,). 3. The capacity now follows from C = q/AV.
- Draw the graph and show complete solutionsLet: q1 = +8 μC , at the originq2 = +6 μC , 6 meters to the right of the originq3 = -86 μC , 8 meters above q2q4 = -0.75 μC , 8 meters above the origin Find the magnitude and direction of the total electric force and total electric field at q3.Two parallel plates, each charged equally and oppositely to the other, are separated by 2.3500 cm. A proton is let go from rest at the positive plate's surface and, at the same time, an electron is let go from rest at the negative plate's surface. What is the distance between the negative plate and the point where the proton and the electron go by each other? Note: unlike most questions, this one will need your answer correct to 5 significant digits