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.
Whan we find out electric potential at distance r , we see that this is same formula of electric potential due to a point charge. So conducting sphere works like a point charge.
A conducting sphere of radius a has a total charge Q on it. 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. 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 with radius R has total charge Q. (a) Find the relationship between the magnitude of the electric field and the electric potential on the surface of the conducting sphere. (Use the following as necessary R, Q, and E for the magnitude of the electric field.) V = (b) For a sphere of radius 77 cm, calculate the maximum surface electric potential at which the surrounding air begins to break down. Take the dielectric strength of (maximum sustainable...
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Consider a charge Q located a distance D>R away from a grounded conducting sphere, where R is the radius of the sphere. Using the method of images, calculate the magnitude and position of the associated image charge. Determine the induced surface charge density of the sphere. .
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...
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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...