A charge q is positioned at point (0,0,d) above a grounded conducting plate (V=0 on the...
A charge q is positioned at point (0,0,d) above a grounded conducting plate (V=0 on the plate). Use the method of images (see lecture notes) to find the electric field on the plate. Since the electric field inside the conductor is zero (charges are not moving), use Gauss’s Law to find the surface charge density σ(r) on the plate and show that the total charge on the plate is –q.
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A charge q is positioned at point (0,0,d) above a grounded
conducting plate (V=0 on the...
3. The above diagram shows a particle, with charge (q) positioned at the center of a...
3. The above diagram shows a particle, with charge (q) positioned at the center of a shell that has surface charge density σ. a) Find the electric field in regions I and II. b) what value of σ s required for the electric field in region II to be zero?
Consider a charge Q located a distance D>R away from a grounded conducting sphere, where R...
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. .
2(25%) An infinite conducting sheet is grounded as shown in the right figure. If a charge,...
2(25%) An infinite conducting sheet is grounded as shown in the right figure. If a charge, Q, stays on the left side of this conductor sheet, D. Please calculate in detail what are the electric field, E, the surface distribution, ob, and the total value, qb, of induced charges.
A conducting plate of metal is charged uniformly so the surface charge per unit area, A...
A conducting plate of metal is charged uniformly so the surface
charge per unit area,
A conducting, plate of metal is charged uniformly so the surface charge per unit area, σ = 6.35 C/m2, (only on the surface!) as in the figure below. Charge on surface of conductor Find the electric field at a distance of 8.26 cm from the plate. N/C.
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...
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)...
6.65 A 10-nC point charge is located at point (0, 0, 10 m) above a grounded...
6.65 A 10-nC point charge is located at point (0, 0, 10 m) above a grounded conducting plane z 0. (a) Find the surface charge density at point (2, -4,0). (b) Calculate the total charge on the plate
4. Two charges are located above a grounded conducting plane defined by 0: a charge q...
4. Two charges are located above a grounded conducting plane defined by 0: a charge q at r 0.0 d) and a charge-21 at r= (d, d, d) . Find the force on the first charge.
(a) We have said that Gauss’s law is always true, but only useful for calculating the...
(a) We have said that Gauss’s law is always true, but only useful for calculating the electric field created by source charge distributions that are spheres, infinite straight cylinders, and infinite flat sheets, and even those cases have additional restrictions. Explain why we are limited to those distributions. Discuss what additional restrictions apply. For example, can we use Gauss’s law to find the field of a sphere whose density depends on distance r from the center? Can we do it...
Problem 2 - Point charge and plane (20 pts) A point charge q (q>0) is located...
Problem 2 - Point charge and plane (20 pts) A point charge q (q>0) is located a distance d above an infinite conducting plane lying in the x-y plane. The plane is connected to the ground (Fig.1), so that the electric potential V at any point on the plane satisfies V=0. Calculating the electric potential generated by the point charge-grounded plane combination at any point P is more complicated than it looks because the conducting plane pulls some electric charge...
3. The above diagram shows a particle, with charge (q) positioned at the center of a shell that has surface charge density σ. a) Find the electric field in regions I and II. b) what value of σ s required for the electric field in region II to be zero?
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. .
2(25%) An infinite conducting sheet is grounded as shown in the right figure. If a charge, Q, stays on the left side of this conductor sheet, D. Please calculate in detail what are the electric field, E, the surface distribution, ob, and the total value, qb, of induced charges.
A conducting plate of metal is charged uniformly so the surface
charge per unit area,
A conducting, plate of metal is charged uniformly so the surface charge per unit area, σ = 6.35 C/m2, (only on the surface!) as in the figure below. Charge on surface of conductor Find the electric field at a distance of 8.26 cm from the plate. N/C.
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...
6.65 A 10-nC point charge is located at point (0, 0, 10 m) above a grounded conducting plane z 0. (a) Find the surface charge density at point (2, -4,0). (b) Calculate the total charge on the plate
4. Two charges are located above a grounded conducting plane defined by 0: a charge q at r 0.0 d) and a charge-21 at r= (d, d, d) . Find the force on the first charge.
Problem 2 - Point charge and plane (20 pts) A point charge q (q>0) is located a distance d above an infinite conducting plane lying in the x-y plane. The plane is connected to the ground (Fig.1), so that the electric potential V at any point on the plane satisfies V=0. Calculating the electric potential generated by the point charge-grounded plane combination at any point P is more complicated than it looks because the conducting plane pulls some electric charge...
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