A thin ring with radius R is placed on the xy plane. The line charge density on the ring is fixed and distributes as 1 sin o (where o = 0 is defined at the +x direction). a) Calculate the electric dipole moment of the ring. b) Write down the electric potential at a point (x, y, z) that is much farther from the origin than R. Express your result as a function of 1, R, x,y,z. (Do NOT use p or ř in your result.)
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- OV 50 V 3. The electric field lines and equipotential lines for a system of charged conductors is shown to the right. Consider the path indicated which begins on a 10V equipotential and ends on a 30V equipotential. a. Complete the table describing the potential and energy changes of different particles as they follow the indicated path. You may express all energy changes, if any, in electron 40 V volts (ev). 30 V 20 V Particle Δν (ν) AU (eV) Proton Electron Neutron b. Estimate the magnitude and direction of the electric field at 75 V points 1 and 2 in the figure. 50 V 25 V OV 1 сm 1 cmA finite rod of length L has total charge q, distributed uniformly along its length. The rod lies on the x-axis and is centered at the orgin. Thus, one endpoint is located at (-L/2,0), and the other located (L/2,0). Define the elctric potential to be zero at an infinite distance away from the rod. a. What is VA, the ectric potential at point A, located at a distance d above the midpoint of the rod on the y-axis? b. What is the VB, the electric potential at point B, located at distance d from one end of the rod (on the x axis)?Consider a slender semicircular ring with a radius of R, possessing a uniform charge distribution resulting in a total charge Q. Determine the electric potential at point A, situated at a distance L from the center of the complete circular arrangement denoted as O. The line segment AO is oriented perpendicular to the plane defined by the ring, as illustrated in the figure below. A. A
- Consider the geometry shown in the figure below. The lengths of the plates in the x and z directions are ∞o. The width of plate 1 in the y direction is L=2. The potential on plates 2 and 3 are 0. The potential on plate 1 is V, = sin² (1) Use separation of variables to find the potential V(x, y). Keep up to 3rd terms. (2) Plot V(x = 0, y) as a function of y. (3) Plot V(x, y = 1) as a function of x. y L=2 V.(y) -Z Plate 1 0 V=0 V=0 Plate 2 Plate 3 XA Martian leaves Mars in a spaceship that is heading to Venus. On the way, the spaceship passes earth with a speed v = 0.76c relative to it. Assume that the three planets do not move relative to each other during the trip. The distance between Mars and Venus is 1.20 × 1011 m, as measured by a person on earth. (a) What does the Martian measure for the distance between Mars and Venus? L = (b) What is the time of the trip (in seconds) as measured by the Martian? Δto =A charged rod has length L and a nonuniform linear charge density λ = cx, where c is a positive constant. Take the left-hand side of the rod to be the origin.Find the electric potential at point P, a distance d above one end. Express your answer in terms of d, L, c, and the Coulomb constant k. Show all steps in your calculation.
- Just the remaining parts pleaseA circular disk with radius R has a constant surface charge density, o. a) Determine the electric potential, V(z), a distance z directly above the center of the disk. 5) From this potential, determine the magnitude of the electric field, E(z)|, a distance z directly above the center of the disk. O Verify that your answer in part b) gives the correct result in the two extreme cases 1) very close to the charged disk (z > R). RA ball of conductor with radius RA = 2 cm is charged + 2Q. The balllocated centrally to the hollow conductor sphere with a charge of –3Q withthe inner radius RB = 4 cm and the outer radius RC = 6 cm (see Figure).a. Using Gauss's Law, calculate the electric field strength atthe points L, M, and N.b. Calculate the electric potential at the point rL = 3 cm and rM = 1 cm
- Separation of Variables: Cartesian coordinates A rectangular metal tube (its height extends from z = 0 to infinity) is placed on the xy plane. See Fig. 1. The side faces of the tube are kept at zero potential, V = 0, and the face of the base, supported on the xy plane, is maintained at a potential Vo (x.y). a) Calculate the potential inside the tube.b)Assume that the base plate, the one that rests on the xy plane, is conductive and maintained at constant potential, that is,Vo (x,y) = V.Calculate the potential inside the tube and determine the density of load o (x, y) on this plate, at z = 0. It might be useful know that: σ = - εo ∂V / ∂nA hollow cylinder of radius r and height h has a total charge q uniformly distributed over its surface. The axis of the cylinder coincides with the z-axis, and the cylinder is centered at the origin, as shown in (Figure 1). What is the potential V0 in the limit as h goes to zero? Express your answer in terms of q, r, and ϵ0. V attached in image 2.Needs Complete typed solution with 100 % accuracy.