(a) How would you place two electrons on a sphere of radius R so that the...
(a) How would you place two electrons on a sphere of radius R so that the electrostatic potential energy is minimized. How would you place three electrons to solve the same problem.
(b) Explain in physical terms how a microwave oven works. What would happen when you put a conductor in the microwave oven? Explain.
Homework Answers
I
put a 1/4 inch thick clear glass container into the microwave with
a plate on top and put it in for almost 5 minutes (there was lots
of soup). When It came out the soup was really hot but I could
still hold the top parts of the container. After measuring the
soup's heat it was about 120-130 degrees but the top part felt cool
to the touch
Microwave ovens deliver heat to things that are electrically conductive, like water that has stuff dissolved in it, which is almost all water. Glass is an insulator, so it doesn't get heated (by the microwaves, it may get heated by the soup). Never put metal objects in a microwave
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(a) How would you place two electrons on a sphere of radius R so
that the...
1. Find the energy stored in a uniformly charged solid sphere of radius R with volume...
1. Find the energy stored in a uniformly charged solid sphere of radius R with volume charge density ρ. Do it two different ways: (a) Use the expression for the electrostatic energy in terms of the potential and the charge density, (b) Use the expression for the electrostatic energy in terms of the square of the electric field, 2 Jall space
Problem 2 Consider a solid sphere of radius R with a uniform charge density with total...
Problem 2 Consider a solid sphere of radius R with a uniform charge density with total charge Q distributed throughout its volume. a) Show that the electric field for this system is given by for r> R Ameoks for TSR b) What is the potential V (r) for the regions () r > R and r S R2 Use lim and remember that V (r) is continuous at r R r)0 as your reference point HINT: You might be able...
Problem 1: A grounded metal sphere with radius R is located at the center of a...
Problem 1: A grounded metal sphere with radius R is located at the center of a linear dielectric sphere with radius 2R. The dielectric has a relative permittivity of &r. The composite sphere is exposed to some external fields, which create a potential V-α cosa where α is a constant Find the electric field and the electric displacement in the dielectric, i.e. R<rc2R. Hint: Use the appropriate boundary (surface) conditions to solve for the potential in that region in terms...
Please help. Thank you. (3.) (40 pts) An insulating sphere of radius a has an embedded...
Please help. Thank you.
(3.) (40 pts) An insulating sphere of radius a has an embedded nonuniform charge den- sity: p(P) = (1+) where pe is a positive constant (this charge density is only valid for r <a). Sur- rounding the sphere, and concentric with it, is a conducting shell of inner radius b> a and outer radius c which is charged (not neutral). I do not know what the charge on the conductor is, but I am told that...
A small, solid conducting sphere of radius r1 sits inside a hollow conducting spherical shell of...
A small, solid conducting sphere of radius r1 sits inside a hollow conducting spherical shell of inner radius r2 and outer radius r3. A potential difference of magnitude V is placed across the inner and outer conductors so that there is a net charge of -Q on the inner conductor and +Q on the outer conductor. Suppose a thin but finite thickness conducting shell was placed between the sphere and the outer shell. This extra shell is electrically isolated. Would...
1. Image charges in sphere We have two charges of magnitude +Q seperated by a distance of 2d, see drawing. a) Find a grounded conducting sphere (potential set to zero) with radius R, where R is the m...
1. Image charges in sphere We have two charges of magnitude +Q seperated by a distance of 2d, see drawing. a) Find a grounded conducting sphere (potential set to zero) with radius R, where R is the minimum radius needed to neutralize the repulsion from the two charges on each other. Hint: Try to reverse engineer the idea of image charges for a sphere which was discussed in the lectures. Place image charges and find an expression for the force....
(a) Imagine a gaussian sphere of radius R with an electron at the center. Write down...
(a) Imagine a gaussian sphere of radius R with an electron at the center. Write down the total flux through the sphere (including the sign) in terms of physical constants and R. (b) Suppose we place a proton a distance 2R from the electron. What is the flux through the original gaussian sphere? (c) How do your answers to parts (a) and (b) change if we replace the gaussian sphere with a cube of width 2R? (d) How do your...
AP Physics C FRQ 3. A sphere of mass m and radius r is released from...
AP Physics C FRQ
3. A sphere of mass m and radius r is released from rest at the top of a curved track of height H. The sphere travels down the curved track and around a loop of radius R. The sphere rolls without slipping during the entire motion. Point A on the loop is at height R, and point B is at the top of the loop. The rotational inertia of the sphere is 2mr2/s. Express all of...
5: Two solid spheres of radius R each have a total charge Q. Sphere A is...
5: Two solid spheres of radius R each have a total charge Q. Sphere A is a conductor and sphere B is an insulator with the charge spread out evenly throughout its volume. The spheres are far from each other so they do not influence each other. Compare the magnitudes of the electric fields at T = for each sphere. Specifically, which is larger and why? Are they zero or nonzero? Explain. Similarly, compare the electric fields at 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"...
1. Find the energy stored in a uniformly charged solid sphere of radius R with volume charge density ρ. Do it two different ways: (a) Use the expression for the electrostatic energy in terms of the potential and the charge density, (b) Use the expression for the electrostatic energy in terms of the square of the electric field, 2 Jall space
Problem 2 Consider a solid sphere of radius R with a uniform charge density with total charge Q distributed throughout its volume. a) Show that the electric field for this system is given by for r> R Ameoks for TSR b) What is the potential V (r) for the regions () r > R and r S R2 Use lim and remember that V (r) is continuous at r R r)0 as your reference point HINT: You might be able...
Problem 1: A grounded metal sphere with radius R is located at the center of a linear dielectric sphere with radius 2R. The dielectric has a relative permittivity of &r. The composite sphere is exposed to some external fields, which create a potential V-α cosa where α is a constant Find the electric field and the electric displacement in the dielectric, i.e. R<rc2R. Hint: Use the appropriate boundary (surface) conditions to solve for the potential in that region in terms...
Please help. Thank you.
(3.) (40 pts) An insulating sphere of radius a has an embedded nonuniform charge den- sity: p(P) = (1+) where pe is a positive constant (this charge density is only valid for r <a). Sur- rounding the sphere, and concentric with it, is a conducting shell of inner radius b> a and outer radius c which is charged (not neutral). I do not know what the charge on the conductor is, but I am told that...
A small, solid conducting sphere of radius r1 sits inside a hollow conducting spherical shell of inner radius r2 and outer radius r3. A potential difference of magnitude V is placed across the inner and outer conductors so that there is a net charge of -Q on the inner conductor and +Q on the outer conductor. Suppose a thin but finite thickness conducting shell was placed between the sphere and the outer shell. This extra shell is electrically isolated. Would...
1. Image charges in sphere We have two charges of magnitude +Q seperated by a distance of 2d, see drawing. a) Find a grounded conducting sphere (potential set to zero) with radius R, where R is the minimum radius needed to neutralize the repulsion from the two charges on each other. Hint: Try to reverse engineer the idea of image charges for a sphere which was discussed in the lectures. Place image charges and find an expression for the force....
AP Physics C FRQ
3. A sphere of mass m and radius r is released from rest at the top of a curved track of height H. The sphere travels down the curved track and around a loop of radius R. The sphere rolls without slipping during the entire motion. Point A on the loop is at height R, and point B is at the top of the loop. The rotational inertia of the sphere is 2mr2/s. Express all of...
5: Two solid spheres of radius R each have a total charge Q. Sphere A is a conductor and sphere B is an insulator with the charge spread out evenly throughout its volume. The spheres are far from each other so they do not influence each other. Compare the magnitudes of the electric fields at T = for each sphere. Specifically, which is larger and why? Are they zero or nonzero? Explain. Similarly, compare the electric fields at r =...
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