Question A1 (12 marks] A sphere with radius R carries a charge density that is proportional...
Consider a charged sphere of radius R. The charge density is not constant. Rather, it blows up at the center of the sphere, but falls away exponentially fast away from the center, p(r)=(C/r2)e-kr where C is an unkown constant, and k determines how fast the charge density falls off. The total charge on the sphere is Q. a) Write down the Electric Field outside the sphere, where r ≥ R, in term of the total Q. b) Show that C=...
A sphere of radius R has total charge Q. The volume charge density (C/m3) within the sphere is ρ(r)=C/r2, where C is a constant to be determined. The charge within a small volume dV is dq=ρdV. The integral of ρdV over the entire volume of the sphere is the total charge Q. Use this fact to determine the constant C in terms of Q and R. Hint: Let dV be a spherical shell of radius r and thickness dr. What...
Q3: Find the electric field inside a spherical sphere which carries a charge density proportional to the distance from the origin ? = fr, for someme constant f. (As you can see this charge density is not uniform, and you must integrate to get the enclosed charge)
A solid, insulating sphere of radius a has a uniform charge density of P and a total charge of Q. Concentric with this sphere is a conducting spherical shell with inner and outer radii are b and c, and having a net charge -3Q. (a) (5 pts.)Use Gauss's law to derive an expression for the electric field as a function of r in the regions r < a (b) (4 pts.) Use Gauss's law to derive an expression for the electric field...
A sphere or radius R has a charge density given by p(r') = kr'. A) Calculate the electric field inside and out. B) Calculate the electric potential using the integral E*dl. C) Calculate the energy stored in this configuration by integrating pVdT.
A sphere has a radius of 50cm and a volume charge density Problem 2: Gauss's Electric Field Law - 25 points Asphere has a radius of 50cm and a volume charge density of P, = 3 uC/m at the origin. and is centered a. Determine the electric field at r = 25cm b. Determine the electric field at r = 50cm C. Determine the electric field at r = 100cm
Guided Problem 4 -Gauss's LawA solid, insulating sphere of radius a has a uniform charge density ρ and a total charge Q. Concentric with this sphere is an uncharged, conducting hollow sphere whose inner and outer radii are b and c as shown in the following figure. (a) Find the magnitude of the electric field in the regions: r<a, a<r<b, and r>c. (b) Determine the induced charge per unit area on the inner and outer surfaces of the hollow sphere.Solution scheme:...
Consider a sphere of radius a with a uniform charge distribution over its volume, and a total charge of q_o. Use Gauss's Law to calculate the electric field outside the sphere, and then inside the sphere. Solve the general problem in r, recognizing that problem spherical symmetry. Draw a graph of the electric field the has the surface of the strength as a function of noting where if the surface of the sphere is (a). Some hints: the surface area...
A sphere of radius R carries a volume charge density ρ(r) = kr, where k is a constant and r is in spherical coordinates. Calculate the energy of this configuration, check the answer by calculating it in four ways.
A solid non-conducting sphere of radius R carries a uniform charge density throughout its volume. At a radial distance r1 = R/2 from the center, the electric field has a magnitude E0. What is the magnitude of the electric field at a radial distance r2 = 3R?