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2. Potentials and a Conducting Surface The electric potential outside of a solid spherical conductor of...
A conducting sphere of radius a, at potential Vo, is surrounded by a thin concentric spherical...
A conducting sphere of radius a, at potential Vo, is surrounded by a thin concentric spherical shell of radius b, over which someone has glued a surface charge density σ(8)-k cos θ, where k is a constant and θ is the polar spherical coordinate. (a) Find the potential in each region: (i)r > b, and () a<r<b. [5 points] [Hint: start from the general solution of Laplace's equation in spherical coordinates, but allow for different coefficients in the radial part...
A spherical metal (conductor) has a spherical cavity in side. There is a single point charge...
A spherical metal (conductor) has a spherical cavity in side. There is a single point charge Q at the cavity center. The total charge on the meta is 0 (a) Describe how the charge is distributed on the E=? sphere. Would the surface charge density be u form at each surface? (b) Draw the electric field lines. c) Find the electric field for a point outside the metal. Express it in terms of r, the distance of the point in...
1 (a) Explain why there is no electic field inside an uncharged, or statically charged, [2]...
1 (a) Explain why there is no electic field inside an uncharged, or statically charged, [2] conductor (b) An uncharged perfectly conducting solid sphere of radius a is placed with its centre at the origin in a region of uniform electric field E = E02. The presence of the sphere modifies the electric field (and the potential) i. Show that the initial potential in spherical coordinates is Vinit (T, 0, )Eor cos 0 everywhere (i.e. before the sphere was placed...
2. (30 POINTS) A spherical shell of radius R holds a potential on its surface of:...
2. (30 POINTS) A spherical shell of radius R holds a potential on its surface of: V(R, 0) = V.(1 + 2cose - cos20) (a.) Find the potential inside and outside the sphere. (b.) Find the surface charge density on the sphere. (c.) Find the dipole moment and the dipole term of the electric field, Epip.
Electric Potential 9-2 1) Picture a conducting sphere with a net positive charge on its surface....
Electric Potential 9-2 1) Picture a conducting sphere with a net positive charge on its surface. Discuss the followin estions with your lab partners. a) Why must all of the excess charge on the conductor reside on the surface of the sphere? b) We know that at equilibrium the electric field inside the conductor must be zero. Does this mean that the electric potential inside the sphere is zero? c) Is the potential changing inside the conducting sphere? d) How...
Select Tru or False. 1. A conducting sphere with charge Q at equilibrium has zero E...
Select Tru or False. 1. A conducting sphere with charge Q at equilibrium has zero E field inside it. The E field outside is the same as that of a point charge Q, E=keQ/r2. The potential outside it is the same as that of a point charge Q. V= keQ/r. (r is the distance to the center). The potential inside the conducting sphere is equal to the potential at its surface. V= keQ/R. (R is the radius of the sphere)...
A thin, uniformly charged spherical shell has a potential of 645 V on its surface. Outside...
A thin, uniformly charged spherical shell has a potential of 645 V on its surface. Outside the sphere, at a radial distance of 21.0 cm from this surface, the potential is 325 V. Calculate the radius of the sphere. Determine the total charge on the sphere. What is the electric potential inside the sphere at a radius of 2.0 cm? Calculate the magnitude of the electric field at the surface of the sphere. If an electron starts from rest at...
5. A hollow sphere of radius R has a potential on the surface of V(θ, d)...
5. A hollow sphere of radius R has a potential on the surface of V(θ, d) Vo cos θ. There is no a) Find the potential everywhere inside and outside the sphere. b) Find the electric field everywhere inside the sphere. (You will find it easier to convert the potential to Cartesian coordinates and then find the field.) c) Find the charge density σ(0) on the surface of the sphere using Gauss' law. charge inside or outside the sphere.
Q4 : The electric potential inside a charged spherical conductor of radious R is given by...
Q4 : The electric potential inside a charged spherical conductor of radious R is given by V = KERA and the potential outside is given by V = ke Q Derive the electric field a)inside b) outside the spherical conductor. ID
Charged sphere in a uniform electric field. Consider the problem of a charged conducting sphere in...
Charged sphere in a uniform electric field. Consider the problem of a charged conducting sphere in the uniform external electric field. This is equivalent to the example from the notes with the added charge on the sphere. Find the electric field in the space outside the sphere. Assume that the sphere has radius R and total charge Q. (a) Since there is no charge in the space outside the sphere, this is obviously the case of Laplacian in the azimuthally...
A conducting sphere of radius a, at potential Vo, is surrounded by a thin concentric spherical shell of radius b, over which someone has glued a surface charge density σ(8)-k cos θ, where k is a constant and θ is the polar spherical coordinate. (a) Find the potential in each region: (i)r > b, and () a<r<b. [5 points] [Hint: start from the general solution of Laplace's equation in spherical coordinates, but allow for different coefficients in the radial part...
A spherical metal (conductor) has a spherical cavity in side. There is a single point charge Q at the cavity center. The total charge on the meta is 0 (a) Describe how the charge is distributed on the E=? sphere. Would the surface charge density be u form at each surface? (b) Draw the electric field lines. c) Find the electric field for a point outside the metal. Express it in terms of r, the distance of the point in...
1 (a) Explain why there is no electic field inside an uncharged, or statically charged, [2] conductor (b) An uncharged perfectly conducting solid sphere of radius a is placed with its centre at the origin in a region of uniform electric field E = E02. The presence of the sphere modifies the electric field (and the potential) i. Show that the initial potential in spherical coordinates is Vinit (T, 0, )Eor cos 0 everywhere (i.e. before the sphere was placed...
2. (30 POINTS) A spherical shell of radius R holds a potential on its surface of: V(R, 0) = V.(1 + 2cose - cos20) (a.) Find the potential inside and outside the sphere. (b.) Find the surface charge density on the sphere. (c.) Find the dipole moment and the dipole term of the electric field, Epip.
Electric Potential 9-2 1) Picture a conducting sphere with a net positive charge on its surface. Discuss the followin estions with your lab partners. a) Why must all of the excess charge on the conductor reside on the surface of the sphere? b) We know that at equilibrium the electric field inside the conductor must be zero. Does this mean that the electric potential inside the sphere is zero? c) Is the potential changing inside the conducting sphere? d) How...
5. A hollow sphere of radius R has a potential on the surface of V(θ, d) Vo cos θ. There is no a) Find the potential everywhere inside and outside the sphere. b) Find the electric field everywhere inside the sphere. (You will find it easier to convert the potential to Cartesian coordinates and then find the field.) c) Find the charge density σ(0) on the surface of the sphere using Gauss' law. charge inside or outside the sphere.
Q4 : The electric potential inside a charged spherical conductor of radious R is given by V = KERA and the potential outside is given by V = ke Q Derive the electric field a)inside b) outside the spherical conductor. ID
Charged sphere in a uniform electric field. Consider the problem of a charged conducting sphere in the uniform external electric field. This is equivalent to the example from the notes with the added charge on the sphere. Find the electric field in the space outside the sphere. Assume that the sphere has radius R and total charge Q. (a) Since there is no charge in the space outside the sphere, this is obviously the case of Laplacian in the azimuthally...
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