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Use Gauss's Law to find the charge enclosed by the cube with vertices
(+/-1, +/-1, +/-1) if the electric field is E(x, y, z) = xi + yj + zk.
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- A 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.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?Consider a thin rod which has a uniformly distributed charge Qot = -1 µC. The rod is bent into a quarter of a circle of radius R = 1 m. Find the x- and y-components of the electric field created by the rod the point O the center of the arc. Hint: The following integrals are useful: cose de = [sin@]% î sine de = [-cos0]% R
- The volume charge density ρ for a spherical charge distribution of radius R= 6.00 mm is not uniform. (Figure 1) shows ρ as a function of the distance r from the center of the distribution. a)Calculate the electric field at r = 1.00 mm. b)Calculate the electric field at r = 1.00 mm.An infinite cylinder of radius R has a linear charge density X. The volume charge density (C/m³) within the cylinder (r< R) is p(r)=rpo/R. where po = 3X/2TR² Part A Use Gauss's law to find an expression for the electric field E inside the cylinder, r < R, in terms of A and R. Express your answer in terms of the variables r, R, A, and 0. E= Submit ΓΙ ΑΣΦ Request Answer Review ?Positive electric charge is uniformly distributed along the y-axis with a linear charge density l. Consider the case where charge is distributed only between points y = +a and y = -a. For points between the +x-axis, graph the x-component of the electric field as a function of x, Ex (x), for values x = a/2 and x = 4a. Consider instead the case where charge is distributed along the entire y-axis with the same charge density l. Using the same graph as in part (a), plot the x-component of the electric field, Ex (x), as function of x for values of x between x = a/2 and x = 4a.
- = Three uniform charge distributions are present in a region: an infinite sheet of charge, a finite line charge, and a ring of charge. The infinite sheet of charge at (x, -3, z), where x and z spans from negative to positive infinity, has a charge density Ps 5 nC/m². The finite line charge at (0, -1, z), where z ranges from -2 to 2, has a charge density -4 nC/m. Finally, the ring of charge, with a radius of 3m and charge density PL 2 nC/m, is parallel to the xz-plane centered at (0, 4, 0). All coordinates are in meters. Use the value k = 9 x 10⁹ in your solutions and = answers. Question: Determine the magnitude the electric field due to the infinite sheet charge only at (0, 2, 0).Consider a line of charge that extends along the x axis from x = -3 m to x = +3 m. The line of charge has a constant linear charge density equal to 6 nC/m (note the nano). Calculate the magnitude of the electric field due to this charge at (0, 5 m), in N/C. Use k = 9 x 109 N m2 / C2. The resulting integral is solved with trigonometric substitution, so solve the integral using a computer if you don't know how to do this. (Please answer to the fourth decimal place - i.e 14.3225)A solid conducting sphere, which has a charge Q1 =84Q and radius rg = 1.5R is placed inside a very thin spherical shell of radius rp = 3.4R and charge Q2 =15Q as shown in the figure below. Q2 Tb Q1 ra Find the magnitude of the electric field at r=6.2. Express your answer using one decimal point in units 1 where k = 4περ of k
- Calculate the electric field in N/C at point P, a distance (4.35x10^1) cm along the central axis of a disk of charge with radius (9.157x10^0) cm, and charge density +(8.0860x10^0) µC/m2. You do not need to enter a unit vector in your answer, but must put a negative sign in, if the electric field is pointing along the negative z-axis. RCharge of a uniform density (11 pC/m?) is distributed over the entire xy plane. A charge of uniform density (6 pC/m2) is distributed over the parallel plane defined by z = 2.0 m. Determine the magnitude of the electric field for any point with z = 3.0 m.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 Exr