Directions: Solve the problems below and show complete solution. 1. Calculate the flux of the electric field E, through the surface A, in each of the three cases shown: a) = b) D- c)
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Topic: Electric flux and Gauss's Law
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- A non-uniform thin rod is bent into an arc of radius R. The linear charge density λ of the roddepends on θ and is given byλ =λ0/cos θwhere λ0 is a positive constant. The arc extends from θ =π/4 to θ =3π/4as shown a)Sketch the direction of the resultant electric field at the origin.b) Calculate the magnitude of the electric field E->.Three chargesbare arranged on a rectangle as shown below. What is the net electric field at P2? Calculate the magnitude and the directionProblem 2: A closed hollow cylinder (i.e., with capped ends) is situated in an electric field given by E(u) = E0(u5i + 7j + 22k). The cylinder’s axis is on the x-axis with its center at the origin. The cylinder’s height is L and its radius is R. Here u = x/x0 is a dimensionless variable, where x0 sets the scale of the field. Refer to the figure. Part (a) Integrate to find an expression for the total electric flux through the cylinder in terms of defined quantities and enter the expression. Part (b) For L = 8.7 m, R = 0.25 m, E0 = 4.5 V/m, and x0 = 1 m, find the value of the electric flux, in units of volt•meter, through the cylinder. Part (c) If the electric field is E(u) = E0(323u2i + 42j + 415k), enter an expression for the total flux in terms of defined quantities.
- 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.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.please do not copy answers from existing problems here and online. answer completely. A ring-shaped conductor with radius a = 2.50 cm has a total positive charge Q = +0.125 nC uniformly distributed around it, as shown The center of the sign is at the origin of coordinates O. (a) What is the electric field (magnitude and direction) at point P, which is on the x-axis at x = 40.0 cm? (b) A point charge q = -2.50 microC is placed at the point P described in part (a). What are the magnitude and direction of the force exerted by the charge q on the ring?
- Part A through part D, please Charge is distibuted uniformly over each of two spherical volumes with radius R. One sphere of charge is centered at the origin and the other at x=2R (Figure 1). Let left-hand sphere have positive charge Q and let the right-hand sphere have negative charge -Q . Part A Find the magnitude of the net electric field due to these two distributions of charge at the point x=0 on the x-axis. Express your answer in terms of the variables Q , R , and appropriate constants. Part B Find the magnitude of the net electric field at the point x=R/2 on the x-axis. Express your answer in terms of the variables Q , R , and appropriate constants. Part C Find the magnitude of the net electric field at the point x=R on the x-axis. Express your answer in terms of the variables Q, R , and appropriate constants. Part D Find the magnitude of the net electric field at the point x=3Ron the x-axis. Express your answer in terms of the variables Q, R, and appropriate constants.The figure below shows a section of a very thin, very long, straight rod with a uniform charge per unit length of λ. Point O is a perpendicular distance d from the rod. A spherical gaussian surface is centered at point O and has a radius R. (Use any variable or symbol stated above along with the following as necessary: ε0.) A)What is the electric flux through the spherical surface if R < d? B)What is the electric flux through the spherical surface if R > d?c. i. Compare the electric flux in a cubical surface of a side 10cm and spherical surface ofradius 10 cm, when a charge of 5µC is enclosed by them.ii. How does the electric field enclosing a given charge vary when the area enclosed bythe charged is doubled. Assuming the electric flux is constant.
- A disk of radius 0.10 m is oriented with its normal vector n at 30 degrees to a unform electric field E vector of a magnitude of 2.0x10^3 N/C. What is the electric flux through the disk? (Provide the complete details for the Illustrated Diagram - inside the box, Given, Required, Equation, Solution, and Answer)1. What is the electric field at any point outside the shell of radius R where a positive charge Q is placed on it? Take r to be the radius of the Gaussian sphere. Explain your answer. (note: k=1/3πε0) A. zero B. kq/R^2 C. kq/r^2 D. kqr^2/R^2 2. What is the electric field at any point inside the shell of radius R where a positive charge Q is placed on it? Take r to be the radius of the Gaussian sphere. Explain your answer. (note: k=1/3πε0) A. zero B. kq/R^2 C. kq/r^2 D. kqr^2/R^2A hollow sphere made from a non-conducting material is shown below in cross-section. The inner radius is R1, and the outer radius is R2. The material is charged uniformly -ρ.(a) Using Gauss’ Law, find an expression in terms R1, R2, and ρ of the magnitude(measured in N/C) and the direction (away from or towards the center) of the electricfield at a distance r from the center of the sphere, for values R1 < r < R2? (Do all thiswork symbolically - don't use the values of part (b) for this part.) (b) The inner radius is R1 = 1.00 cm, and the outer radius is R2 = 4.00 cm. Thematerial is charged uniformly ρ = -1.70 nC/m3. If the electric potential is 0V infinitely faraway, what is the electric potential at the outer surface (r = R2) of the sphere? Please show full work Thank you!