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Problem 2 - Point charge and plane (20 pts) A point charge q (q>0) is located...
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.
A point charge Q with charge 10nC is located at (2,-1,4) meters in free space. A point charge Qwith charge 1OnC is located at (2,-1,4) meters in free space. An intinite grounded conductor plote is placed along the xey Calculate the eletric freld CE) at point PCI,-,2) meters plane as shoun in the figure V=0 plane (KY) of A point charge Qwith charge 1OnC is located at (2,-1,4) meters in free space. An intinite grounded conductor plote is placed along...
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.
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...
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.
Can someone carefully explain question A and B in detail, please? 5.2 A uniform linear charge density λ is placed on an infinitely long wire. The wire is parallel to an infinite grounded plane, and a distance b above that plane. To make things specific, the points on the wire are described as (x, 0, b), and the conducting plane is z 0. A. Find the potential V(O, y, z) for z > 0. B. Find the induced charge density...
3. (20) A spherically symmetric charge distribution creates the following electric field (2) E E,r with 20 r r < a for 4meoa3 (3) E,= Q 4mor2 for r> a where Q and a are positive constants of suitable units. (a) Draw a graph of E, for 0 <r3a; please label your graph clearly (b) Calculate the charge distribution that generates this electric field. (c) Draw a graph of the charge distribution for 0 <r< 3a; please label your graph...
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
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...
(a) A consequence of the Average Potential Theorem is that all extrema of the electric potential occur on the boundary surface S of a volume V. Use this together with Gauss' law to prove that for a charge-free region of space whose boundaries have well defined potentials, the solution to Laplace's equation is unique 2. 5] (b) Apply the uniqueness theorem in part (a) to calculate the surface charge density that is induced on a grounded conducting plate of infinite...