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A cubical box (sides of length a) consists of five metal plates, whichare welded together and grounded (Fig. 3.23). The top is made of a separate sheetof metal, insulated from the others, and held at a constant potential
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Introduction to Electrodynamics
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- way,one of the two infinite conductive planes grounded parallel to the xz plane is at y=0 and the other at y= π. The surface at x=0 is held at potential V0. Find the potential of the system. (I added the mathematical expressions, which are the continuation of the question, to the photo., thanks)arrow_forwardConsider a rod of length L carrying a charge of q distributed uniformly over its length. Where applicable, let V(r → ∞) = 0. Hint q a. What is the voltage V at point P (at distance a away from the near end of the rod) due to the charge over the length of the rod? Express your answer in terms of given parameters (L,q,a) and physical constants (ke, Eo). Use underscore ("_") for subscripts and spell out Greek letters. Hint for (a) E = Vp = b. Calculate the electric field at point P by differentiating V with respect to a. Let positive sign of E indicate direction of electric field pointing away from the rod. Hint for (b) a Question Help: Message instructor Submit Question с MacBook Pro G Search or type URL ☆ +arrow_forwardThis one is tougher! A sphere of radius r has charge q. (a) What is the infinitesimal increase in clectric potential energy dU if an infinitesimal amount of charge dq is brought to infinity to the surface of the sphere? (b) An uncharged sphere can acquire a total charge Q by the transfer of charge dq over and over and over. Use your answer to part a to find an cxpression for the potential energy of a uniformly-charged sphere of radius R with total charge Q. Answer: U = 3_1 Q² 5 4tc0 R' (c) Your answer to part b is the amount of energy nceded to assemble a charged sphere. It is often called the self-energy of the sphere. What is the self-energy of a proton, assuming it to be a charged sphere with a diamcter of 1.0 x 10 15 m?arrow_forward
- Lets say there is a spherical thin shell of radius a. It carries uniform surface chargewith a density of ps C/m2, (p is ro). I want to find the potential V for points outside the spherical shell and inside the shell. (The reference point for V is set at infinity.) Plot V as a function of R. Thank you for helping me with this practice.arrow_forwardAnswer All.Compute for the work done, in millijoules, in moving a 9-nC charge radially away from the center from a distance of 3 m to a distance of 7 m against the electric field inside a solid insulating sphere of radius 11 m and total charge 7 mC.Ans: -8.5199Determine the total potential energy, in microjoules, stored in a parallelepiped of dimensions are 9 m by 6 m by 8 m if the electric field inside is given as E = 17 ar + 19 aθ + 15 aϕ V/m. Use the permittivity of free space as 8.854 × 10-12 F/m.Ans: 1.6734If the electric field in the region is given as E = -cos(θ) sin( 4 Φ) aθ + b cos( 4 Φ) aφ V/m. Determine the potential at point A(4 m, 0.46 rad, 2.07 m), in volts, if the potential at point B(4 m, 1.00 rad, 0.10 m) is 60 volts. The value of b is also the coefficient of Φ.58.4552 Compute for the potential difference, in volts, in moving a charge from A(3, 2, -2) m to B(7, -6, 6) m against the electric field due to a disk charge of radius 9 m on the plane x = 0. The disk has a…arrow_forwardProblem 3.01. (a) Find the electric field between two plates which are separated along the y-axis Ay = 6.00 mm, where the bottom plate has a potential V₂ = 150. mV and the top plate has a potential V₁ = 5.00 mV. (b) What is the potential at a distance Ay' = 2.00 um from the bottom plate?arrow_forward
- What is the magnitude of the electric field on the axis of the annulus for x>0? Express your answer in terms of a, b, σ, x, and Coulomb constant k.arrow_forward2. 2 A circular portion is cut from a nonconducting disk of radius R₂ = 15.0 cm, with radius R₁ = 4.0 cm measured from the origin of coordinates. The resulting disk, presented in the figure, is loaded its surface with +3Q uniformly, with Q = 4.3 pc. R₂ R₁ B I Then, find the value of the electric potential generated by the disk at point A, located at 20.0 cm from the origin of the coordinate system. And, if an object charged (considered as a point charge) with -1.8 µC is placed on the point A and moves to point B, located 24.0 cm from the origin of the system of coordinates, what is the minimum work required to move the charged object from A to B?arrow_forward6sine 6cose Problem #5: Given the electric fiekd intensity vector E = R R? (V/m), R? A) Find the ekctric potential of point C with respect to point D if C (2 m, a/2, 1/2) and D (4 m, a/2, T/2). Sketch points Cand D, and the integration path taken. B) Find the electric potential of point B with respect to point D if B (2 m, a2, 0) and D (4 m, /2, T2). Sketch points B and D and the integration path taken. C) Find the electric potential of point A with respect to point D if A (2 m, 45°, 90°) and D (4 m, 90 *,90°). Sketch points A and D and the integration path taken. (Points A, B, C and D are in spherical coordinates).arrow_forward
- PA line of length L has a positive charge Q uniformly distributed over it. It is placed on the coordinate axes as shown. Note that the y axis bisects the line. Point P is placed a distance a 7. on the y axis from the line. Construct (but do not solve!) an integral to find the electric potential at point P. Include limits and express the integrals in terms of the given variables, constants, and the integration variable, x. х. +y a +x -L/2 L/2arrow_forwardImagine that two parallel plates are charged to achieve a voltage difference Vo between the plates. They have area A and spacing d. The plates are then electrically isolated so that no charge can be added or taken away. A good conductor of thickness d/2 is placed in between the two plates, as shown. How great is the charge density on the surface of the conductor relative to that on either of the plates? Why? (You may use infinite plane approximations for the surfaces.)arrow_forwardPlease answer parts (a) and (b), showing all work.arrow_forward
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