Problem 6: Assume uniform distribution of charge within a sphere with radius R. Determine the total force with which the southern hemisphere acts on the northern hemisphere. Show your solution in terms of radius of the sphere R and the total charge Q. State assumptions if any
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Problem 6: Assume uniform distribution of charge within a sphere with radius R. Determine the total force with which the southern hemisphere acts on the northern hemisphere. Show your solution in ter...
3. (5 pts) Electrostatic force. A sphere of radius R which carries a uniform volume charge densit...
3. (5 pts) Electrostatic force. A sphere of radius R which carries a uniform volume charge density ρυ is cut in half as shown in the following figure. Find the force that the southern hemisphere exerts on the northern hemisphere and express it in terms of the total charge of the sphere q.
3. (5 pts) Electrostatic force. A sphere of radius R which carries a uniform volume charge density ρυ is cut in half as shown in the following...
2. Spherical Dipole - The surface charge density on a sphere of radius R is constant, +0, on the entire northern hemisphere, and-oo on the entire southern hemisphere. There are no other charges prese...
2. Spherical Dipole - The surface charge density on a sphere of radius R is constant, +0, on the entire northern hemisphere, and-oo on the entire southern hemisphere. There are no other charges present inside or outside the sphere. (a) (4 pts) Compute the dipole moment of that sphere (with the +z-axis up through the pole of the positive, +Oo, hemisphere). Use the definition of a dipole moment, p-Jr, (7)dr', which in this case becomes p:-:J20(7)dA. Write your final answer...
held. A solid sphere has a radius R. The top hemisphere carries a uniform charge density...
held. A solid sphere has a radius R. The top hemisphere carries a uniform charge density p while the lower hemisphere has a uniform charge density of -p. Find an approximate formula for the potential outside the sphere, valid at distances r >> R. A solid sphere has a radius R. The top hemisphere carries a uniform charge density p while the lower hemisphere has a uniform charge density of -p. Find an approximate formula for the potential outside the...
Problem 1: Dipole moment. We have a sphere of radius R with a uniform surface charge...
Problem 1: Dipole moment. We have a sphere of radius R with a uniform surface charge density +ao over the northern hemisphere, and -oo over the southern hemisphere (oo is a positive constant). There are no other charges present inside or outside the sphere. Compute the dipole moment p of this charge distribution assuming the z-axis is the symmetry axis of the distribution. Does p depend on your choice of origin? Why or why not? Are any components of p...
A sphere of radius R has total charge Q. The volume charge density (C/m3) within the...
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...
A solid sphere of radius R has a nonuniform charge distribution p=Ar², where A is a...
A solid sphere of radius R has a nonuniform charge distribution p=Ar², where A is a constant. Determine the total charge, Q, within the volume of the sphere. Please explain and show work Thank you
(a) A sphere with radius R rotates with constant angular velocity . A uniform charge distribution...
(a) A sphere with radius R rotates with constant angular velocity . A uniform charge distribution is fixed on the surface. The total charge is q. Calculate the current density in this scenario where . Show how the E-field is calculated using Gauss' Law and the direction (in spherical coordinates) of the current density. We were unable to transcribe this imageWe were unable to transcribe this image7 =
A sphere of radius R has total charge Q. The volume charge density (C/m^{3}) within the...
A sphere of radius R has total charge Q. The volume charge
density (C/m^{3}) within the sphere
is \(\rho=\rho_{0}(1-(r^{2}/R^{2}))\)
This charge desity decreases quadratically
from \(\rho_{0}\)
b) Show that the electric field inside the sphere points
radially outward with
magnitude
c) Show that your results of part (b) has the expected value at
r=R.
Q1. SEPARATION OF VARIABLES - SPHERICAL SIGMA The surface charge density on a sphere (radius R) i...
Q1. SEPARATION OF VARIABLES - SPHERICAL SIGMA The surface charge density on a sphere (radius R) is a constant, σ0 (As usual, assume V(r = ∞) = 0, and there is no charge anywhere inside or outside, it's ALL on the surface!) i) Using the methods of section 3.3.2 (i.e. explicitly using separation of variables in spherical coordinates), find the electrical potential inside and outside this sphere. ii) Discuss your answer, explain how you might have just "written it down"...
A solid, insulating sphere of radius a has a uniform charge density throughout its volume and a total charge of Q.
A solid, insulating sphere of radius a has a uniform charge density throughout its volume and a total charge of Q. Concentric with this sphere is an uncharged, conducting hollow sphere whose inner and outer radii are b and c as shown in the figure below. We wish to understand completely the charges and electric fields at all locations. (Assume Q is positive. Use the following as necessary: Q, ε0 , a, b, c and r. Do not substitute numerical...
3. (5 pts) Electrostatic force. A sphere of radius R which carries a uniform volume charge density ρυ is cut in half as shown in the following figure. Find the force that the southern hemisphere exerts on the northern hemisphere and express it in terms of the total charge of the sphere q.
3. (5 pts) Electrostatic force. A sphere of radius R which carries a uniform volume charge density ρυ is cut in half as shown in the following...
2. Spherical Dipole - The surface charge density on a sphere of radius R is constant, +0, on the entire northern hemisphere, and-oo on the entire southern hemisphere. There are no other charges present inside or outside the sphere. (a) (4 pts) Compute the dipole moment of that sphere (with the +z-axis up through the pole of the positive, +Oo, hemisphere). Use the definition of a dipole moment, p-Jr, (7)dr', which in this case becomes p:-:J20(7)dA. Write your final answer...
held. A solid sphere has a radius R. The top hemisphere carries a uniform charge density p while the lower hemisphere has a uniform charge density of -p. Find an approximate formula for the potential outside the sphere, valid at distances r >> R. A solid sphere has a radius R. The top hemisphere carries a uniform charge density p while the lower hemisphere has a uniform charge density of -p. Find an approximate formula for the potential outside the...
Problem 1: Dipole moment. We have a sphere of radius R with a uniform surface charge density +ao over the northern hemisphere, and -oo over the southern hemisphere (oo is a positive constant). There are no other charges present inside or outside the sphere. Compute the dipole moment p of this charge distribution assuming the z-axis is the symmetry axis of the distribution. Does p depend on your choice of origin? Why or why not? Are any components of p...
A sphere of radius R has total charge Q. The volume charge
density (C/m^{3}) within the sphere
is \(\rho=\rho_{0}(1-(r^{2}/R^{2}))\)
This charge desity decreases quadratically
from \(\rho_{0}\)
b) Show that the electric field inside the sphere points
radially outward with
magnitude
c) Show that your results of part (b) has the expected value at
r=R.
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