College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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- Below is a solid sphere of insulating materials (meaning that once placed, charge will not move around even when it feels a force). This sphere has a changing charge density given by the equation below. This tells you that there is more charge near the outer edges (when r is larger) then near the center (when r is small) since the charge density is proportional to r^2. In the image R is the total radius of the sphere and r is the distance from the center you will be asked about. There values are below. You have to calculate the amount of charge enclosed with the radius of r to find the electric field. You'll need to integrate to do this - that's where the charge density equation below will be used. Use Gauss's Law to find the Electric Field magnitude at a distance r from the center of the sphere. Make sure to think about charge enclosed and how to find it. It is a little more complicated in this problem. Be careful with your 2 radial values (R and r).arrow_forwardQuestion 2 A 43.8 cm long rod has a nonuniform charge density given by the equation A(z) = Ae-2/b, where A = 2.50 nC/cm and b= 14.0 cm. What is the total charge on the rod? Hint: This problem requires integration! + + + + ++ Total charge on rod: +arrow_forwardA total amount of positive charge Q is spread onto a thin non-conducting circular annulus of inner radius a and outer radius b. The charge is distributed in a way so that the charge density per unit area is given by ? =??3, where r is the distance from the center of the annulus to any point on it and k is a constant.(a) Find an expression for the total charge Q on the annulus. (b) Find an expression for the potential V at the center of the annulus in term of Q, a and barrow_forward
- A cylindrical shell of length l and inner radius a and outer radius b carries a volume charge density given by ρ(r) = α/r where r is the distance to the axis of the shell and α a positive constant. Determine the total charge carried by the shell.arrow_forwardTwo very large, nonconducting plastic sheets, each 10.0 cm thick, carry uniform charge densities 01, 02, 03 and 04 on their surfaces, as shown in the following figure.These surface charge densities have the values o1 = -5.30 µC/m2, o2-5.00µC/m2, o3 = 2.90 µC/m2, and 04-4.00μC/m2. Use Gauss's law to find the magnitude and direction of the electric field at the following points, far from the edges of these sheets. Part A: What is the magnitude of the electric field at point A, 5.00 cm from the left face of the left-hand sheet? Express your answer to three significant figures and include the appropriate units.arrow_forwardTwo very large, nonconducting plastic sheets, each 10.0 cm thick, carry uniform charge densities 01, 02, 03 and 04 on their surfaces, as shown in the following figure (Figure 1). These surface charge densities have the values 01 = -5.50 μC/m², 02 = 5.00 μC/m², 03 = 1.00 μC/m², and 4 = 4.00 μC/m². Use Gauss's law to find the magnitude and direction of the electric field at the following points, far from the edges of these sheets. Part A What is the magnitude of the electric field at point A, 5.00 cm from the left face of the left-hand sheet? Express your answer with the appropriate units. E = O μA Value Units ?arrow_forward
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