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Can you please solve the problem in the picture, Part D. Show all of your work in pictures please.
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- A long copper cylindrical shell of inner radius 2 cm and outer radius 3 cm surrounds concentrically a charged long aluminum rod of radius 1 cm with a charge density of 4 pC/m. All charges on the aluminum rod reside at its surface. The inner surface of the copper shell has exactly charge to that of the aluminum rod while the outer surface of the copper shell has the same charge as the aluminum rod. Find the magnitude and direction of the electric field at points that are at the following distances from the center of the aluminum rod: (a) 0.5 cm, (b) 1.5 cm, (c) 2.5 cm, (d) 3.5 cm, and (e) 7 cm.As shown in Figure, a particle of charge +Q produces an electric field of magnitude Epart at point P, atdistance R from the particle. As in figure b, that same amount of charge is spread uniformly along a circulararc that has radius R and subtends an angle ?. The charge on the arc produces an electric field of magnitudeEarc at its center of curvature P. For what value of ? does Earc = 0.50 Epart ?In Figure 1, an insulating rod is bent into a semicircle of radius R. A charge -Q is uniformly distributed along its top half (for 0 < theta < pi/2) while a charge +Q is uniformly distributed along its bottom half (for -pi/2<theta< 0). Find the lectrostatic force in unit vector notation, acting on an electron with charge -e which is located at the origin O.
- In the figure below, a small, nonconducting ball of mass m = 1.4 mg and charge q = 2.2 ✕ 10−8 C (distributed uniformly through its volume) hangs from an insulating thread that makes an angle θ = 27° with a vertical, uniformly charged nonconducting sheet (shown in cross-section). Considering the gravitational force of the ball and assuming that the sheet extends far vertically and into and out of the page, calculate the surface charge density σ of the sheet. ___________C/m2A +7.00 µC particle is located at x = 0.0 cm, and a –9.0 μC particle is located at x = 40.0 cm. Where must a positive test charge be placed along the x–axis so that the net electric force on it is zero? Hint: In a FBD, place the test charge left of x = 0 cm, in between the two source charges, and right of x = 40 cm. Sketch the direction and relative magnitude of the net force at each location and determine where it might be possible for the net force to be zero. Then set the magnitudes of the forces equal to each other.Consider a thin-shelled hollow tube of length L, radius R with a uniform surface charge of density ? and with the x axis as its central axis. This can be described by: y2+z2=R2 and 0<= x <= L. What is the elctric field at x0 along the x axis, where x0 > L?
- A uniform charge of 16.0 mC is on a thin circular ring lying in an xy plane and centered on the origin.The ring’s radius is 3.00 cm. If point A is at the origin and point B is on the z axis at z = 4.00 cm, what is VB - VA?A very small sphere with positive charge q=+ 5.00 μC is released from rest at a point 1.70 cm from a very long line of uniform linear charge density λ=+ 2.00 μC/m . What is the kinetic energy of the sphere when it is 3.90 cm from the line of charge if the only force on it is the force exerted by the line of charge? Express your answer with the appropriate units. K = ?A very long insulating cylinder of radius R carries a non-uniform charge density, ρ(r) = αr. a) Determine the ~E at all points in space. b) Determine the potenial at all points in space.
- This is a theoretical problem: Imagine a disk of uniformly distributed charge Q with radius R in the plane Z-Y, with its center in the coordinate origin. There's a point P at a distance X (on the X axis).Now imagine a ring of uniformly distributed charge Q with radius R in the plane Z-Y, with its center in the coordinate origin. There's a point P at a distance X (on the X axis). Q, R, and P (thus X) are equal in both cases. Which of these is true for he electrical field on the point P: E(disk) < E(ring) E(disk) > E(ring) E(disk) = E(ring) E(disk) = E(ring)/2 The given information is not enough to make a comparison. Justify your answer for each possibility.A conducting sphere of 3.0 cm radius has a cavity of 2.0 cm radius and sharing the samecenter. First,– 10 nC of charge is dropped on the sphere. Then a + 8.0 nC point charge isintroduced at the center of the cavity. a) How much charge is at the inside surface of the sphere, after the point charge wasplaced at the center? Justify your answer using Gauss’ Law. b) How much charge is at the outer surface of the sphere, after the point charge wasplaced at the center? Justify your answer. c) Calculate and show the direction of the net electric field at 1.0 cm, and at 4.0 cmfrom the center, after the point charge was placed at the center.A solid conducting sphere is surrounded by a thick, spheical conducting shell. Assume that a total charge +Q+Q is placed at the center of the sphere and released. a) After equilibrium is reached, the inener surface of the shell will have b) In terms of QQ, how much charge is on the interior, surface, inner surface, outer surface of the shell?