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Consider the left side of the box as Consisting of N small pieces. Let
Write an expression for the net electric flux
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- The nonuniform charge density of a solid insulating sphere of radius R is given by = cr2 (r R), where c is a positive constant and r is the radial distance from the center of the sphere. For a spherical shell of radius r and thickness dr, the volume element dV = 4r2dr. a. What is the magnitude of the electric field outside the sphere (r R)? b. What is the magnitude of the electric field inside the sphere (r R)?arrow_forwardSections AB and CD of a thin non-conducting ring of radius R are uniformly (with constant linear density) charged with charge + q and −q, respectively. The points ABCD form the vertices of the square. Find the electric field in the center of the ring.arrow_forwardAn insulating sphere of radius a is placed at the center of a spherical conductor whose inner radius is b and outer radius is c (see figure). The +Q charge is uniformly distributed throughout the insulator sphere, while the spherical shell is -Q charged. Find the electric field strength E as a function of the radial distance r, a. inside the insulator ball (r<a) b. in a<r<b c. inside the spherical shell (b<r<c) d. outside the shell (r>c) e. How much charge on the inner surface of the spherical conductor (r= b), and how much on the outer surface of the spherical conductor (r = c)?arrow_forward
- An insulating sphere of radius a is placed at the center of a spherical conductor whose inner radius is b and outer radius is c (see figure). The +Q charge is uniformly distributed throughout the insulator sphere, while the spherical shell is -Q charged. Find the electric field strength E as a function of the radial distance r, d. outside the shell (r>c) e. How much charge on the inner surface of the spherical conductor (r= b), and how much on the outer surface of the spherical conductor (r = c)?arrow_forwardTwo rings of radius R-5 cm are 34 cm apart and concentric with a common vertical axis (figure below). Ring 1 carries a uniformly distributed charge Q₁ = 20 nC and ring 2 carries a uniformly distributed charge of Q₂ = -70 nC. T A Ring 2 Ring 1 1. Find the magnitude of the electric field E created by Ring 1 at point A, halfway between the two rings. E₁ = [N/C] What is the direction of the electric. 2. field E, created by Ring 1 at point A. Direction: + 3. Write the expression of the electric filed E₁ created by Ring 1 at point A. E₁ = [N/C] > [N/C] 7. If vector E₁ = [N/C] and vector Ē₂ = [N/C]. Find the net electric filed Enet at point A. Ēnet = [N/C] 8. If a charge q = 5 nC is placed at location A, what would be the force on this charge? Use the answer of question 7.arrow_forwardA solid insulating plastic sphere of radius a carries atotal net positive charge 3Q uniformly distributed throughout its interior.The insulating sphere is coated with a metallic layer of inner radius a andouter radius 2a. The conducting metallic layer carries a net charge of -2Q. Apply Gauss’s law to find the magnitude of the electric field in the region r < a. Inthe figure, draw the Gaussian surface you are using, and indicate on that surface the direction of anyvectors which appear in the mathematical expression of Gauss’s law. Express your answer in terms ofa, Q, r, and ε0. (If you get an expression involving ρ, substitute it from above to re-express youranswer in terms of the stated variables.)arrow_forward
- A plane with a circular hole of radius R is uniformly charged with areal density o. Find the strength E of the electric field on the axis of the hole as a function of the distance h to its center. Hint: Use the principle of wwwmm superposition.arrow_forwardAn insulating solid sphere of radius a has a uniform bulk density ρ and a total positive charge Q. Calculate the magnitude of the electric field at a point outside the sphere.arrow_forwardConsider an infinitely long, hollow cylinder, with inner radius R1 and outer radius Ra. the material of the cylinder is uniformly charged so that the cylinder has a charge per length. Finally, consider a solid cylinder of radius R, with a uniform charge density. What is the magnitude of the electric field inside the cylinder at a distance r from the center (r<R)?arrow_forward
- 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 ?arrow_forwards of the 15.13 The Coaxial Cable. A long coaxial cable con- sists of an inner cylindrical conductor with radius a and an outer coaxial cylinder with inner radius b and outer eld also radius c. The outer cylinder is mounted on insulating supports and has no net charge. The inner cylinder has a uniform positive charge per unit length A. Calculate the electric field a) at any point between the cylinders, a distance r from the axis; b) at any point outside the outer cylinder. c) Graph the magnitude of the electric field as a function of the distance r from the axis of the cable, from r=0 to r = 2c. d) Find the charge per unit length on the inner surface and on the outer surface of -ntained by the can you %3D the outer cylinder.arrow_forwardIn a uniform electric field of magnitude E, the field lines cross through a rectangle of area A at an angle of 32.9° with respect to the plane of the rectangle. What is the flux through the rectangle?arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning