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A thin rod of length, L, is placed on the +x axis with its left end on the origin (0,0) as show in the diagram to the right. The rod has a charge +Qspread uniformly along its length. The point P is on the x axis a distance r from the origin.
a.Set up the integral to find the electric field at point P.Clearly show your steps.
b.Compute the electric field at point P.
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- A very large thin plane has uniform surface charge density σσ. Touching it on the right (see the figure) is a long wide slab of thickness dd with uniform volume charge density ρEρE.(Figure 1) Determine the electric field to the left of the plane. Assume EE is positive if the field is directed to the right and negative if the field is directed to the left. Express your answer in terms of some or all of the variables σσ, ρEρE, dd, and appropriate constants.The angle between the two short sides is 90°. The two short sides of the triangle have length a. Investigate the net force on the charge (q) in the lower right corner due to the other two charges (q, -q). As needed, assume a right-handed coordinate system shown below: (A) What is the magnitude of the net force on the charge in the lower right corner due to the other charges? Use symbols for the answer. (B) Make a sketch of the net force vector on the x-y axes below with the tail of the arrow at the origin. Label the angle with the x-axis. What quadrant does the vector lie in? Your picture should indicate the correct quadrant.A hemispherical surface of radius b = 16.5m is fixed in a uniform electric field of magnitude E0 = 6.47 V/m. This is illustrated in the attached image. (x - axis points out of the screen) What is the general expression for an infinitesimal area dA, is spheral coordinates (r, Θ, Φ), where Θ is the polar angle and Φ is the azimuthal angle? Use ñ as your outward pointing unit vector. Calculate the electric flux in volt meters through the hemishpere.
- Three chargesbare arranged on a rectangle as shown below. What is the net electric field at P2? Calculate the magnitude and the directionWhat are the strength and direction of the electric field at the position indicated by the dot in the figure A) What is the strength of the electric field? Let r = 5.4 cm. B)Specify the direction of the electric field as an angle below the horizontal.A semicircle of radius a is in the first and second quadrants, with the center of curvature at the origin. Positive charge +Q is distributed uniformly around the left half of the semicircle, and negative charge −Q is distributed uniformly around the right half of the semicircle in the following figure. What is the magnitude and direction of the net electric field at the origin produced by this distribution of charge?
- What is the net electric flux through the cylinder (a) shown in (Figure 1)? What is the net electric flux through the cylinder (b) shown in (Figure 2)? Express your answer in terms of the variables E, R, and the constant π.F3.) For diagram A, What is the magnitude of the totalelectric field, at point P? (round to the proper sigfigs)Use GFSA (Given, Find, Solution, and Answer) on the given space below. Encircle your final answer, write it in scientific notation with 2 decimal places (if possible). An cylinder with radius 1 m and length 1.5 m has an infinite line of charge with a linear charge density of 30 C/m. (Make an illustration of the problem) (a) What is the total charge enclosed by the Gaussian cylinder? (b) What is the electric flux through the cylinder due to the infinite line of charge? (c) Calculate the electric field at a point 3 m away from the infinite line of charge.