4. Two charges are located above a grounded conducting plane defined by 0: a charge q...
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.
There is a grounded conducting plane on the xy plane and a grounded hemisphere of radius R, in the positive z-axis, centered at the origin. We put a point charge +Q on the z-axis, and its distance from the origin is S. Find the force on the point 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...
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
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....
Q 7. (5 pts) Consider two semi-infinite grounded conducting planes (one is in the x-z plane stretching from x = 0 to infinity, the other is in the y-z plane stretching from y = 0 to infinity) and a point charge +Q located at (a, b), as shown to the right. Suppose we want to use the method of images to solve for the charge distribution on the grounded planes. (Note: do not perform this calculation! Just provide responses for...
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. .
LSM 1 A point charge Q-10 mC is located at I m from a grounded conducting plate as shown in the figure. Assuming that the plate is infinitely large, calculate the force exerted on the charge Data Go-10 /36x F/m) Justify your answer 1m
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. .
We observe two point charges in the yz-plane: one of them has charge 2q and is located in (x,y,z)-(0,0,a) and the other has a charge of -3q and is located in (x,y,z)-(0,b,a) a) Calculate the dipole moment p, and p, for the two charges around (0,0,0), and sketch for a-2, b-3, c -1, the vector for the total dipole moment p for the configuration In addition to the two point charges, we now have an infinite grounded conductor placed in...