Q1. The volume charge density of a spherical shell with inner radius a and outer radius b is given as Pv = Po/R as shown in Figure 1. Determine E in all regions. (po is a positive constant) Pu Figure 1
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- A nonconducting spherical shell has an inner radius A, an outer radius B, and a nonuniform charge density given by p(r) sindr where B and a are constants. r3 The inner spherical shell is surrounded with a concentric nonconducting spherical shell that has an inner radius B, outer radius C, and a uniform charge density such that the electric field for r> C is zero. What is the total charge contained in the inner spherical shell? b. What is the charge density in the outer spherical shell? c. What is the magnitude of the electric field for A2. Consider that a multiple charge distributions exists in free space where at point P(0,1,1) the electrostatic field is given with E = 26, %3D a) Based on the given Electrostatic field at point P, define the sources using at least two different charge distributions (charge distribution could be either point charge, surface charge, line charge or volume charge). Write explicitly the locations, types and values of the charge distributions. b) For the defined charge distribution, write the electric field and potential at the origin of the coordinate system.6. A cylinder with radius R and infinite length is centered on the z-axis and has a uniform charge density r R p= Po 0 where po is a constant. a) Using Gauss's law find the electric field for r R. Express your answer in terms of the charge per unit length of the cylinder (you'll have to think about how to define it). Hint: in terms of symmetry, this case is very similar to an infinite line charge. b) Now a uniform surface charge density o is pasted onto the surface of the cylinder such that the electric field outside the cylinder is zero. What is o in terms of R, po, and numerical factors?Q3) Working with Charge Densities a) A finite line of charge is 20 cm long and has a uniformly distributed charge of +4 C. What is its linear charge density, 2? b) A spherical shell has a radius of 20 cm and uniformly distributed charge of +4 C. What is its surface charge density, o? c) A spherical insulator has an outer radius of 20 cm and has an empty hole inside (concentric with the spherical insulator) with a radius of 10 cm. The insulator has a uniformly distributed charge of +4 C. What is its volume charge density, p? d) A cylindrical shell with no end caps has a radius of 20 cm, length of 1.2 m, and a uniformly distributed charge of +4 C. What is its surface charge density, ơ? f) A metal square with sides equal to 20 cm has a uniformly distributed charge of +4 C. What is its surface charge density, o?6. An infinite line is uniformly charged with a linear charge density A.Find a formula describing the electric field at a distance z from the line.1) Calculate the voltage in a spherical conductor. You need to use the integral form of AV. O + The conductor is effectively a point charge from outside the conductor. This problem is far out. Start from infinity and come up to the surface of the conductor imagining there is a point charge in the middle of the conductor. Use this information to set a up and integral form for AV. Then solve. Then apply the fact that the V = const in a conductorA charged sphere with radius 7m has a net charge of 2 μC. If you were to evaluate the electric field at a distance of 2 m, what would be the charge enclosed by your gaussian surface? Note: Use a spherical gaussian surface A. 3.50e-7 C B. 1.16e-7 C C. 4.66e-8 C D. 2.10e-7 CProblem 10 A sphere has a constant interior charge density p. What is the electric field for all values of r? Inside and outside? Plot the strength of the electric field as a function of r.4. An insulating ball has a charge of 6 µC/m3. The sphere has a radius of 40 cm and it has a cavity around its center with a radius of 10 cm. Remember that k = 9 x 109 Nm2/C2, and use π = = 3.14. A. What is the total charge of the insulating ball ? ........µC B. What is the magnitude of the electric field at a distance of 4 cm from the center ?............ N/C C. What is the magnitude of the electric field at a distance of 50 cm from the center ? ..........N/C Please solve sub parts A,B,C and no reject. Im needed max 30 minutes thank u2. Consider an insulating spherical shell of inner radius a and outer radius b. a. If the shell has a net charge Q uniformly distributed over its volume, find the vector electric field in all regions of space (r b) as a function of r. b. Now assume that the shell has a non-uniform charge density given by r2 p(r) = Po ab What is the net charge of the shell? c. For the charge distribution in part (b), find the vector electric field in all regions of space (r b) as a function of r.a line ofPictured below is a spherical conducting ball of radius a surrounded by a spherical non-conducting "thick" shell of inner radius b and outer radius c. The conducting ball has a total charge of Q1 and the non-conducting shell has a total charge of Q2 uniformly distributed throughout its volume (i.e., the volume charge density p for the shell is constant) a. Determine the volume charge density p of the non-conducting shell. b. Determine the electric field at a point a distance r from the center of the conducting ball. Consider separately each case: p < a, a C. c. If Q2 = - 2Q1, for which values of r is the electric field zero? Can you show all work part a b and cSEE MORE QUESTIONS