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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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- An infinitely large horizontal plane carries a uniform surface charge density n = -0.280 nC/m². What is the electric field ✓? A proton is traveling in this field with initial speed strength in the region above the plane [Select] V01.00 x 105 m/s at 0 = 30° angle with respect to the plane, as shown in the figure below. Use the coordinate system in ✓? If the zero potential is the figure and neglect the effect of gravity. How high can the proton go [Select] at the origin level, i.e., y = 0 level, what is the potential energy [Select] height y21.00 m [Select] y [Select] 0 of the proton when it is at a height of y₁ = 0.500 m ? What is the proton's kinetic energy at Vo V 0 and kinetic energy X
*arrow_forward*Two infinite grounded metal plates lie parallel to the xz plane, one at y = 0, the other at y = a, as shown below in Fig. 2 (next page). The left end, at x = 0, is closed off with an infinite strip insulated from the two plates and is maintained at an electric potential V(0,y,z) = Eo-y. Find the electric potential everywhere inside the slotted region. a V = Ey YA V=0 V=0*arrow_forward*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_forward* - The space between the plates of a parallel-plate capacitor (Fig. 4.24) is filled with two slabs of linear dielectric material. Each slab has thickness a, so the total distance between the plates is 2a. Slab-1 has dielectric constant of 2 and slab-2 has a dielectric constant of 1.5. With the area of each of the top and bottom conducting plates is much greater than a?, we can assume the the surface charge densities +o and -o on the top and bottom plates is uniform. (a) Find the electric displacement D in each slab. (b) Find the electric field E in each slab. (c) Find the potential difference between the plates. (d) Find the locations and amounts of all bound charge. (e) Based on the values of bound charge, recalculate E and verify your answer from (b). (f) How do your results relate to the formula for the addition of two series capacitors?
*arrow_forward*Consider 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_forward*This 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* - Answer 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_forward*Problem 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*Consider a uniformly charged solid sphere of radius ? and total charge ? centered on the origin. In this problem you will calculate the potential ?(?) for ? < ? in two different ways. Use infinity as the reference point (i.e., ?(∞) = 0). (a) Use Eq. 2.21 of Griffiths to compute the potential at ? < ?. (b) Use Eq. 2.29 of Griffiths to compute the potential at ? < ?.*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_forward*For problem 11 of the text, calculate the potential in pixpoV at a point r = 0.398 R from the center of the sphere. (5 sig figs)*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/2*arrow_forward*

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