A parallel plate capacitor of width w, length L, and separation d has a solid dielectric slab of permittivity e(x) as shown in the figure. A potential difference Vo Volts is applied to the capacitor terminals. Neglecting fringing, for i. e(x) = €, ii. e(x) = €ge* Determine; a) The electric field intensity Ē, b) The displacement vector D, c) The capacitance C, d) The stored electrostatic energy We e) Magnitude and the direction of the force acting on the slab Fm
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- The uniform electric field E in the air outside the plane boundary of an LIH dielectric material is at an angle of 30° to the normal to the The relative permittivity & of the dielectric is 3.0. Find the angle that the electric field in the dielectric makes with the normal. Clearly state any boundary conditions that you boundary, as shown in Figure 2. use. 30° Eair air dielectric € = 3.0) Consider an infinitely long cylinder with radius R and uniform surface charge density o. a. Find the magnitude of the electric field at a distance s from the axis of the cylinder for s R. c. Using your answer to part b, find the potential difference between two points: s= a and s = b. thor axis with its1) Calculate the voltage in a spherical conductor. You need to use the integral form of AV. O + The conductor is effectively a point charge from outside the conductor. This problem is far out. Start from infinity and come up to the surface of the conductor imagining there is a point charge in the middle of the conductor. Use this information to set a up and integral form for AV. Then solve. Then apply the fact that the V = const in a conductor
- A solid ball of radius r has a uniform charge density p. Correct Part C Let E (r) represent the electric field due to the charged ball throughout all of space. Which of the following statements about the electric field are true? Check all that apply. ► View Available Hint(s) E(0) = 0. E(rb) = 0. lim,→∞ E(r) = 0. The maximum electric field occurs when r = 0. The maximum electric field occurs when r = b. The maximum electric field occurs as r →→∞. SubmitConsider a particle of charge q = 2.4 C and mass m = 1.5 kg passing through the region between a pair of infinitely long horizontal plates separated by a distance d = 4.5 m with a uniform electric field strength E = 36 N/C directed in the downwards direction (-y direction). The particle begins moving horizontally with an initial velocity of v = 25 m/s from a position halfway between the plates. A.How far horizontally in meters will the particle travel before striking one of the plates. B.Caculate the speed in meters per second,with which the particle will strike the plate. C.Suppose that the eletric field is directed upward instead of downward.Caculate the new horizontal distance, in meters, that the particle travels before striking one the plates.answer for (d) and (e) please
- The picture on the right shows a plate capacitor. You may assume that the two plates are very large compared to the separation between the plates (i.e. you may treat them as 'infinite' planes). The plates are charged to ±Q, each plate has an area of A, and the plates are separated by a distance d. The x-axis in this problem is pointing from the negative to the positive plate, with the origin at the negative plate. The electric field at point 2 has a magnitude of E. E=3000 A=1 m² d = 8 mm c. What is the electric field strength at point 1? d. What is the charge Q on the plates? ·area A IT +Q €0=8.85 x 10-12 -a X=0 e. What is the electric field strength at point 3? Part A: a. In the picture, sketch the electric field between the plates by drawing the field lines. b. Find the surface charge density n on each plate. Nm² 12 x(mm)An electron is projected with an initial speed v0 = 1.70×106 m/s into the uniform field between the parallel plates in (Figure 1). Assume that the field between the plates is uniform and directed vertically downward, and that the field outside the plates is zero. The electron enters the field at a point midway between the plates. If the electron just misses the upper plate as it emerges from the field, find the magnitude of the electric field. Express your answer in newtons per coulomb. Suppose that in the figure the electron is replaced by a proton with the same initial speed v0v0. Would the proton hit one of the plates? What would be the direction of proton's displacement? displacement is upward displacement is downwardH
- Consider a solid uniformly charged dielectric sphere where the charge density is give as ρ. The sphere has a radius R. Say that a hollow of charge has been created within the spherethat is offset from the center of the large sphere such that the small hollow has its center on the x axis where x = R/2. Using a standard frame where the large frame has its center at the origin, find the Electric field vector at the following points. a.The origin b.Anywhere inside the hollow (challenging) c.x = 0, y = R d.x = -R, y =0I need help can you label which one is A,B,C and DA cube has sides of length L = 0.370 m. It is placed with one corner at the origin as shown in the figure (Figure 1). The electric field is not uniform but is given by E =( -5.69 N/(C. m) )æi+( 3.20 N/(C · m) )zk. Part A Find the electric flux through each of the six cube faces Sı, S2, S3, S4, S5, and Sg- Enter your answers numerically separated by commas. ν ΑΣφ D1, Þ2 , D3 , Þ4 , Þ5 , Þ6 = (N/C) - m² Submit Request Answer Part B Find the total electric charge inside the cube. q = Figure 1 of 1 Submit Request Answer S2 (top) S6 (back) Provide Feedback S1 (left side) L - S3 (right side) y L L. S4 (bottom) S3 (front)