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.
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- Question 1 Four stationary electric charges produce an electric field in space. The electric field depends on the magnitude of the test charge used to trace the field O has different magnitudes but same direction everywhere in space is constant everywhere in space has different magnitude and different directions everywhere in space CANADFind the position vector r(arrow) that points from Proton 1 to the Proton 2, its magnitude |r(arrow)∣, and its unit vector, r(hat). Look at the image for the question.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.
- A thin rod is bent into a half circle of radius R and centered on the y-axis so that it lies flat in the xy-plane as indicated in the diagram. This glass rod is rubbed all over with silk so that the rod has a total positive charge Q uniformly distributed over the length of the bent rod. Answer the following questions to determine the net electric field at an observation location A located on the positive z-axis a distance d from the origin. (See pic 1 for the following questions) A. Consider an infinitesimal piece of the glass rod located at an angle θ\thetaθ from the positive x-axis. Determine the relative position vector that points from this piece of the rod to the observation location. B. Derive an expression for the electric field dE⃗ of the infinitesimal piece dQ located at angle θ and integrate over the charge distribution to determine the net electric field E⃗ at the observation location. Your answer should only contain the given variables (R, Q, d) and known…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 downwardConsider 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 =0
- Positive charge is distributed with a uniform density λ along the positive x-axis from r to ∞, along the positive y-axis from r to ∞, and along a 90° arc of a circle of radius r, as shown below. What is the electric field at O? (Use the following as necessary: λ, r, and ε0.) E = _____ i + ______ j + ______ kIn 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.Part A and B
- Shown in the figure below is a collection of two charges labeled as q, and q2. Also labeled is the "Point P", which is where we will do our calculations. To understand the notation, please note the following: not to scale y 9₁ (0, V₂) Item Charge (C) P P (0, y₂) The vector E means the electric field at P due only to gr The vector E means the electric field at P due only to q The vector Er means the total electric field at P due to all charges (x,y) m (0.00,5.62) None q1 -7.41e-06 (0.00, -1.56) q2 4.28e-06 (2.56, 2.94) 9₂ (x₂, V₂) Determine the distance from q; to P: r₁= Determine the distance from q₂ to P: r₂-Please don't provide handwritten solution ......Please help