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Consider a charge Q located a distance D>R away from a grounded conducting sphere, where R...
13.2. Consider a charge Q located close to a grounded conducting sphere centered(a) at the origin....
13.2. Consider a charge Q located close to a grounded conducting sphere centered(a) at the origin. The sphere is of radius a, and the charge is located at-= d, where d> a. (a) Show that an image charge Qi--a0d located a12-a2/d satisfies the condition V = 0 at the surface of the sphere. (b) Determine the surface charge density ρ(0) induced on the surface of the sphere. (c) Determine the total charge induced on the surface of the sohere. .
A conducting sphere with radius R is centered at the origin. The sphere is grounded having...
A conducting sphere with radius R is centered at the origin. The sphere is grounded having an electric potential of zero. A point charge Q is brought toward the sphere along the z- axis and is placed at the point ะ-8. As the point charge approaches the sphere mobile charge is drawn from the ground into the sphere. This induced charge arranges itself over the surface of the sphere, not in a uniform way, but rather in such a way...
A conducting sphere of radius a has a total charge Q on it. A charge q...
A conducting sphere of radius a has a total charge Q on it. A charge q is brought at a distance d from the center of the sphere (d > a). Using the method of images: (a) Find the electric potential V (r, θ) in the region r > a. (b) Find the surface charge density on the surface of the sphere. (c) Find the force on the charge q.
Using the method of images, discuss the problem of a point charge q inside a hollow,...
Using the method of images, discuss the problem of a point
charge q inside a hollow, grounded, conducting sphere of inner
radius a. Find,
a) the potential inside the sphere;
b) the induced surface-charge density;
c) the magnitude and direction of the force acting on q.
d) Is there any change in the solution if the sphere is kept at
a fixed potential V? If the sphere has a total charge Q on its
inner and outer surfaces?
Using the...
1. A hollow conducting sphere of radius R has a charge Q placed on its surface....
1. A hollow conducting sphere of radius R has a charge Q placed on its surface. A point charge Q1 is placed at a distance d> R from the center of the sphere. a) Using the method of superposition, find a combination of two image charges inside the sphere that result in the correct electric field and potential outside the sphere. b) What is the force between the sphere and the point charge? What is the force whern 0, and...
A conducting sphere of radius a is kept at a constant potential V0. A charge q...
A conducting sphere of radius a is kept at a constant potential V0. A charge q is brought at a distance d from the center of the sphere (d > a). Using the method of images: (a) Find the electric potential V (r, θ) in the region r > a. (b) Find the surface charge density on the surface of the sphere. (c) Find the force on the charge q.
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....
Calculate the potential due to a point charge q in the presence of a conducting sphere...
Calculate the potential due to a point charge q in the presence of a conducting sphere at constant potential V. Radius of conducting sphere is R. The point charge is situated at a distance b from the center of the sphere (b>R) ( Image charge for a grounded conducting sphere is given ; q' = -(Rq)/b and distance r'= R^(2)/b
There is a conducting sphere of radius R, and electric potential VR. An infinite distance away,...
There is a conducting sphere of radius R, and electric potential VR. An infinite distance away, V infinity = 0. Show that the sphere's surface charge density is given by
Only need help with (d) = 0 ( [this point is away from 0] A conducting...
Only need help with (d)
= 0 ( [this point is away from 0] A conducting sphere of radius a is hollow and grounded (V = 0). A particle of charge q is a placed inside at a distance b from the center. We wish to find the potential anywhere inside the sphere. This problem can be solved with the image charge method. The image charge d' should be placed a distance b = from the center, so that the...
13.2. Consider a charge Q located close to a grounded conducting sphere centered(a) at the origin. The sphere is of radius a, and the charge is located at-= d, where d> a. (a) Show that an image charge Qi--a0d located a12-a2/d satisfies the condition V = 0 at the surface of the sphere. (b) Determine the surface charge density ρ(0) induced on the surface of the sphere. (c) Determine the total charge induced on the surface of the sohere. .
A conducting sphere with radius R is centered at the origin. The sphere is grounded having an electric potential of zero. A point charge Q is brought toward the sphere along the z- axis and is placed at the point ะ-8. As the point charge approaches the sphere mobile charge is drawn from the ground into the sphere. This induced charge arranges itself over the surface of the sphere, not in a uniform way, but rather in such a way...
Using the method of images, discuss the problem of a point
charge q inside a hollow, grounded, conducting sphere of inner
radius a. Find,
a) the potential inside the sphere;
b) the induced surface-charge density;
c) the magnitude and direction of the force acting on q.
d) Is there any change in the solution if the sphere is kept at
a fixed potential V? If the sphere has a total charge Q on its
inner and outer surfaces?
Using the...
1. A hollow conducting sphere of radius R has a charge Q placed on its surface. A point charge Q1 is placed at a distance d> R from the center of the sphere. a) Using the method of superposition, find a combination of two image charges inside the sphere that result in the correct electric field and potential outside the sphere. b) What is the force between the sphere and the point charge? What is the force whern 0, and...
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....
There is a conducting sphere of radius R, and electric potential VR. An infinite distance away, V infinity = 0. Show that the sphere's surface charge density is given by
Only need help with (d)
= 0 ( [this point is away from 0] A conducting sphere of radius a is hollow and grounded (V = 0). A particle of charge q is a placed inside at a distance b from the center. We wish to find the potential anywhere inside the sphere. This problem can be solved with the image charge method. The image charge d' should be placed a distance b = from the center, so that the...
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