A non-uniform, but spherically symmetric, distribution of charge has a charge density ρ(r) given as follows: ρ(r)=ρ0(1−4r/3R) for r≤R ρ(r)=0 for r≥R ρ0 is a positive constant Obtain an expression for the electric field in the region r ≤ R
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A non-uniform, but spherically symmetric, distribution of charge has a charge density ρ(r) given as follows: ρ(r)=ρ0(1−4r/3R) for r≤R ρ(r)=0 for r≥R ρ0 is a positive constant
Obtain an expression for the electric field in the region r ≤ R
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- Positive charge is distributed in a sphere of radius R that is centered at the origin. Inside the sphere, the electric field is Ē(r) = kr-1/4 f, where k is a positive constant. There is no charge outside the sphere. a) How is the charge distributed inside the sphere? In particular, find an equation for the charge density, p. b) Determine the electric field, E(r), for r > R (outside the sphere). c) What is the potential difference between the center of the sphere (r = 0) and the surface of the sphere (r = R)? d) What is the energy stored in this electric charge configuration?The charge density of a non-uniformly charged sphere of radius 1.0 m is given as: For rs 1.0 m; p(r)= Po(1-4r/3) For r> 1.0 m; p(r)= 0, where r is in meters. What is the value of r in meters for which the electric field is maximum?If there is a a non-uniform, but spherically symmetric, distribution of charge has a charge density ρ(r) given as follows: ρ(r)=ρ0(1−4r/3R)f or r≤R ρ(r)=0 for r≥R where ρ0 is a positive constant. What is the expression for the electric field in the region r <= R?
- The volumetric charge density of a cylinder of radius R is proportional to the distance to the center of the cylinder, that is, ρ = Ar when r≤R, with A being a constant. (a) Sketch the charge density for the region - 3R < r < 3R. What is the dimension of A?b) Calculate the electric field for a point outside the cylinder, r > Rc) Calculate the electric field for a point inside the cylinder, r<R.d) Sketch ExrA cylinder of length L=5m has a radius R=2 cm and linear charge density 2=300 µC/m. Although the linear charge density is a constant through the cylinder, the charge density within the cylinder changes with r. Within the cylinder, the charge density of the cylinder varies with radius as a function p( r) =p.r/R. Here R is the radius of the cylinder and R=2 cm and p, is just a constant that you need to determine. b. Find the constant po in terms of R and 2. Then plug in values of R and 1. to find the value for the constant p. c. Assuming that L>>R, use Gauss's law to find out the electric field E inside the cylinder (rR) in terms of 1. and R. d. Based on your result from problem c, find the electric field E at r=1cm and r=4cm.The volume charge density of a spherical charge distribution is given by ρ(r)=ρ0e−ar where ρ0 and a are constants. Write an expression for the magnitude of the electric field valid for all r
- Electric charge is distributed over the disk x2+y2 ≤4 so that the charge density at (x,y) is δ(x,y)=3x+3y+3x2 +3y2 (measured in coulombs per square meter). Find the total charge on the disk.A charge distribution creates the following electric field throughout all space: E(r, 0, q) = (3/r) (r hat) + 2 sin cos sin 0(theta hat) + sin cos p (phi hat). Given this electric field, calculate the charge density at location (r, 0, p) = (ab.c).Two homogeneous rods with a length of 5 cm each are positioned as in Fig. a. Determine the magnitude and direction of the electric field vector at point P on the coordinates (5.0) cm, if the unit charge density is λ = 2.10-9 C / m! b. If an electron is placed at point P, what is the electric force that is experienced by the electron?
- QUESTION 1 Problem: An infinitely long cylindrical conductor has radius R and uniform surface charge density o. In terms of R and o, what is the charge per unit length A for the cylinder? Answer: A = 2A thick insulating spherical shell of inner radius a=2.4R and outer radius b=6.1R has a uniform charge density p. pR What is the magnitude of the electric field at r=5.6 R ? Express your answer using one decimal place in units of €oA thick insulating spherical shell of inner radius a=2.1R and outer radius b=9.9R has a uniform charge density p. pR What is the magnitude of the electric field at r=4.5 R ? Express your answer using one decimal place in units of