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1 (a) Explain why there is no electic field inside an uncharged, or statically charged, [2]...
If you can draw a FBD as well 70. When an uncharged conducting sphere of radius...
If you can draw a FBD as well
70. When an uncharged conducting sphere of radius a is placed at the origin of an xyz coordinate system that lies in an initially uniform electric field E = E, Î, the resulting electric potential is V(x, y, z) = V, for points inside the sphere and E, az V(x, y, z) = V. – Eoz + (x2 + y2 + z2)3/2 for points outside the sphere, where V, is the (constant)...
2. Potentials and a Conducting Surface The electric potential outside of a solid spherical conductor of...
2. Potentials and a Conducting Surface The electric potential outside of a solid spherical conductor of radius R is found to be V(r, 9) = -E, cose (--) where E, is a constant and r and 0 are the spherical radial and polar angle coordinates, respectively. This electric potential is due to the charges on the conductor and charges outside of the conductor 1. Find an expression for the electric field inside the spherical conductor. 2. Find an expression for...
I have already solved for the correct answers on #1,and #2; however, I have not been...
I have already solved for the correct answers on #1,and #2; however, I have not been able to get answers for #3,#4, and #5. A solid insulating sphere of radius a = 4 cm is fixed at the origin of a co-ordinate system as shown. The sphere is uniformly charged with a charge density ρ = -114 μC/m3. Concentric with the sphere is an uncharged spherical conducting shell of inner radius b = 12.9 cm, and outer radius c =...
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.
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...
3. A Little Bundle of Jey Charge: The electric field of a solid bal of charge,...
3. A Little Bundle of Jey Charge: The electric field of a solid bal of charge, Q, with radius R is given by: T E (a) Calculate the divergence of E g spherical coordinates and components) at a point inside and a point outside the sphere to show that you obtain the correct result from Gauss's law V.E-) (b) Assume a reference point of roo e., V(oo)). Detere the electric potential at all (c) Now assume a reference point of...
FIG. 2. Setup of Exercise 3 Exercise 3 The electrostatic potential of an electic dipole moment...
FIG. 2. Setup of Exercise 3 Exercise 3 The electrostatic potential of an electic dipole moment d located at the origin takes the following form d-T Tr where r is the vector joining the origin to the point X (7 is called the "position vector" in the textbook). See Fig. 2 (i) Chosing the z axis to be aligned with the electric dipole moment, express φ in terms of cartesian, cylindrical, (ii) The electric field is obtained from E-- Compute...
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...
1. (3 points) An electron is initially at rest in a uniform electric field of 2.5...
1. (3 points) An electron is initially at rest in a uniform electric field of 2.5 V/m. What will be the velocity of the electron 10 seconds later? 2. (3 points) Two spherical cavities a and b are hollowed out from the interior of a neutral conducting sphere of radius R 50 cm. The radii of cavities a and b are Ra 10 cm and R 20 cm. A point charge of a +30 uC is placed at the center...
i) If the total charge enclosed inside a Gaussian surface is zero, then E everywhere on...
i) If the total charge enclosed inside a Gaussian surface is zero, then E everywhere on the Gaussian surface must be zero. Circle one: True, False. Explain very briefly if you wish: ii) A spherical region (radius R, centered on the origin) has electric field E(r)=0 throughout. The voltage V(r) must also vanish throughout that region. Circle one: True, False. Explain very briefly if you wish: iii) A spherical region (radius R, centered on the origin) has voltage V(r) =...
If you can draw a FBD as well
70. When an uncharged conducting sphere of radius a is placed at the origin of an xyz coordinate system that lies in an initially uniform electric field E = E, Î, the resulting electric potential is V(x, y, z) = V, for points inside the sphere and E, az V(x, y, z) = V. – Eoz + (x2 + y2 + z2)3/2 for points outside the sphere, where V, is the (constant)...
2. Potentials and a Conducting Surface The electric potential outside of a solid spherical conductor of radius R is found to be V(r, 9) = -E, cose (--) where E, is a constant and r and 0 are the spherical radial and polar angle coordinates, respectively. This electric potential is due to the charges on the conductor and charges outside of the conductor 1. Find an expression for the electric field inside the spherical conductor. 2. Find an expression for...
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.
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...
3. A Little Bundle of Jey Charge: The electric field of a solid bal of charge, Q, with radius R is given by: T E (a) Calculate the divergence of E g spherical coordinates and components) at a point inside and a point outside the sphere to show that you obtain the correct result from Gauss's law V.E-) (b) Assume a reference point of roo e., V(oo)). Detere the electric potential at all (c) Now assume a reference point of...
FIG. 2. Setup of Exercise 3 Exercise 3 The electrostatic potential of an electic dipole moment d located at the origin takes the following form d-T Tr where r is the vector joining the origin to the point X (7 is called the "position vector" in the textbook). See Fig. 2 (i) Chosing the z axis to be aligned with the electric dipole moment, express φ in terms of cartesian, cylindrical, (ii) The electric field is obtained from E-- Compute...
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...
1. (3 points) An electron is initially at rest in a uniform electric field of 2.5 V/m. What will be the velocity of the electron 10 seconds later? 2. (3 points) Two spherical cavities a and b are hollowed out from the interior of a neutral conducting sphere of radius R 50 cm. The radii of cavities a and b are Ra 10 cm and R 20 cm. A point charge of a +30 uC is placed at the center...
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