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- Suppose a capacitor consists of two coaxial thin cylindrical conductors. The inner cylinder of radius ra has a charge of +Q, while the outer cylinder of radius rb has charge -Q. The electric field E at a radial distance r from the central axis is given by the function:.... pls fill in the blanksA. Give the physical interpretation of the gradient, divergence and rotational theorems. B. Using the Dirac-delta function, find the electric field and electrostatic potential that will occur in the center of a uniformly charged hemispherical layer of radius A (surface charge density).Consider 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.
- At the surface of any conductor in electrostatic equilibrium, E=o/ɛ0. Show that this equation is consistent with the fact that E=kq/r at the surface of a spherical conductor.In empty space (εr = 1), the region x1 <x <x2 is filled with material with dielectric coefficient εr = 6 as a planar infinitely large plate. The geometry is shown in the figure below. Pay attention to the coordinate system placement. Region I: In (x <x1), the electric field vector E1 = (- 3.5) ux + (-5.5) uy + (5.5) uz has been observed. II. Region: The relative dielectric constant at (x1 <x <x2) is r = 6. III. Region: By determining the electric field E3 at (x2 <x) (space εr = 1), |E3| write its value numerically.C) The lightning is formed when current starts to flow between the two spheres. Explain at least two different non obvious facts about what is going on inside and around these “lightning bolts”. If a direction is involved with your facts, give that direction.
- Solve a,b Thanks. Use the following constants if necessary. Coulomb constant, k = 8.987×10^9 N⋅ m^2/C^2 . Vacuum permittivity, ϵ0 = 8.854×10^−12 F/m . Magnitude of the Charge of one electron, e = −1.60217662×10^−19 C . Mass of one electron, me = 9.10938356×10^−31 kg . Unless specified otherwise, each symbol carries their usual meaning. For example, μC means microcoulomb .In empty space (εr = 1), the region x1 <x <x2 is filled with material with dielectric coefficient εr = 4 as a planar infinitely large plate. The geometry is shown in the figure below. Pay attention to the coordinate system placement. I. Region: In (x <x1) the electric field vector is observed as E1 = (- 1.5) ux + (-5.5) uy + (-8.5) uz. II. Region: (x1 <x <x2) de εr = 4 By determining the electric field E2, write the value of the x-component: E2x numerically.In empty space (er = 1), the region x1 <x <x2 is filled with material with a dielectric coefficient er = 4 as a planar infinitely large plate. The geometry is shown in the figure below. Pay attention to the coordinate system placement.Region I: In (x <x1), the electric field vector is observed as E1 = (- 0.5) ux + (5.5) uy + (-1.5) uz.Region II : By determining (x1 <x <x2) value er = 4 electric field E2,|E2|,write its value numerically.
- An electric dipole that is completely free to move (both rotation and translation) is placed in a region of uniform electric field. The dipole moment makes an angle of 30° to the direction of the electric field. Which of the following statements is correct? The total force on the dipole is zero, but the total torque is non-zero. O Both the total torque and total force on the dipole are zero. O The total torque on the dipole is zero. Both the total force and the total torque on the dipole are non-zero. The total torque on the dipole is zero, but the total force on the dipole is non-zero.Which of the following is true regarding the parallel-plate capacitor? The surface charge densities on the plates are unequal in magnitude and opposite in polarity. O The electric field between the plates is always nonzero. Elsewhere, the electric field is zero. The electric field between the plates is always zero. Elsewhere, the electric field is nonzero. O The electric field anywhere, whether between the two plates or outside, is always nonzero. O The electric field anywhere, whether between the two plates or outside, is always zero.In empty space (er = 1), the region x1 <x <x2 is filled with material with a dielectric coefficient Er = 7 as a planar infinitely large plate. The geometry is shown in the figure below. Pay attention to the coordinate system placement.Region I: Electric field vector at (x <x1) E1 = (6.5)ux + (0.5)uy+(7.5)uz has been observed.Region II : The relative dielectric constant at (x1 <x <x2) is r = 7.Region III: By determining the electric field E3 at (x2 <x) (space er = 1), | E3 |write its value numerically.