Consider a thin-shelled hollow tube of length L, radius R with a uniform surface charge density σ and with the z-axis as its central axis. This can be described by: x2 + y2 = R2 and -L/2 ≤ z ≤ L/2. What is the electric field at z0 along the z-axis, where z0 > L/2?
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Consider a thin-shelled hollow tube of length L, radius R with a uniform surface charge density σ and with the z-axis as its central axis. This can be described by: x2 + y2 = R2 and -L/2 ≤ z ≤ L/2. What is the electric field at z0 along the z-axis, where z0 > L/2?
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- A long, nonconducting, solid cylinder of radius 4.0 cm has a nonuniform volume charge density r that is a function of radial distance r from the cylinder axis: r =Ar2. For A = 2.5 mC/m5, what is the magnitude of the electric field at (a) r = 3.0 cm and (b) r = 5.0 cm?Figure (a) shows a narrow charged solid cylinder that is coaxial with a larger charged cylindrical shell. Both are nonconducting and thin and have uniform surface charge densities on their outer surfaces. Figure (b) gives the radial component E of the electric field versus radial distance r from the common axis. The vertical axis scale is set by E; = 3.9 x 10° N/C. What is the linear charge density of the shell?A spherical insulator with radius R is centered at the origin. The volume charge density p of the insulator is non-uniform and varies with position according to p(r) = ar, where a is a constant. Derive an expression for the electric field E(r) for all points outside the sphere (r > R). Hint: finding the total charge of the sphere will require an integral.
- A long nonconducting cylinder (radius 6.0 mm) has a nonuniform volume charge density given by ar, where a= 6.2 mC/m' and r is the distance from the axis of the cylinder. What is the magnitude of the electric field at a point 2.0 mm from the axis?It has an uneven volumetric charge density p (r) = ar ^ 2 (a: constant) on an insulating sphere of radius a and charge Q1. This sphere is surrounded by a conductive spherical shell of inner radius b and outer radius c. It is Q2 on the shell. Calculate the magnitude of the electric field in the regions r c.A charge distribution that is spherically symmetric but not uniform radially produces an electric field of magnitude E = Kr4, directed radially outward from the center of the sphere. Here r is the radial distance from that center, and K is a constant.What is the volume density r of the charge distribution?
- A cross section of long cylindrical structure with hollow core is shown in Fig. Q3. A radial section of (b – a) mm thickness is filled with volume charge density p, C/m³. Find the expression of the electric field intensity within regions r < a and a < r < b. Then, determine the electric field intensity at G,z). Note that z is an arbitrary point on the z-axis. а y P, C/m? a Fig. Q3Figure (a) shows a narrow charged solid cylinder that is coaxial with a larger charged cylindrical shell. Both are nonconducting and thin and have uniform surface charge densities on their outer surfaces. Figure (b) gives the radial component E of the electric field versus radial distance r from the common axis. The vertical axis scale is set by E, -4.2 x 10³ N/C. What is the linear charge density of the shell? E₂ (a) Number 0 r(cm) (6) Units 10.8 C/m^2An infinitely long, cylindrical, insulating shell of inner radius a and outer radius b has a uniform volume charge density r. A line of uniform linear charge density l is placed along the axis of the shell. Determine the electric field for (a) r , a, (b) a , r , b, and (c) r . b.
- A sphere of radius 2a is made of a nonconducting material that has a uniform volume charge density p. Assume that the material does not affect the electric field. A spherical cavity of radius a is now removed from the sphere as shown in the figure below. Show that the electric field within the cavity is uniform and is given by E0 and Ey - pa/3.Figure (a) shows a narrow charged solid cylinder that is coaxial with a larger charged cylindrical shell. Both are nonconducting and thin and have uniform surface charge densities on their outer surfaces. Figure (b) gives the radial component E of the electric field versus radial distancer from the common axis. The vertical axis scale is set by E, -4.5 x 10° N/C. What is the linear charge density of the shell? Number E r(cm) (A) Units 13.8a) A solid sphere, made of an insulating material, has a volume charge density of ? = a/r, where r is the radius from the center of the sphere, a is constant, and a > 0. What is the electric field within the sphere as a function of the radius r? Note: The volume element dV for a spherical shell of radius r and thickness dr is equal to 4?r2dr. (Use the following as necessary: a, r, and ?0.) b.) What If? What if the charge density as a function of r within the charged solid sphere is given by ? = a/r^2? Find the new magnitude and direction of the electric field within the sphere at radius r. (Use the following as necessary: a, r, and ?0.)