menu
bartleby
search
close search
Hit Return to see all results

Two infinite grounded parallel conducting planes are separated by a distance d. A point charge q is placed between the planes. UseGreen's reciprocation theorem to prove that the total induced charge on one of the planes is equal to -q times the fractional perpendiculardistance of the point charge from the other plane. (Hint: As your comparison electrostatic problem with the same surfaces choose one|whose charge densities and potential are known and simple.)

Question

3

Two infinite grounded parallel conducting planes are separated by a distance d. A point charge q is placed between the planes. Use
Green's reciprocation theorem to prove that the total induced charge on one of the planes is equal to -q times the fractional perpendicular
distance of the point charge from the other plane. (Hint: As your comparison electrostatic problem with the same surfaces choose one
|whose charge densities and potential are known and simple.)
help_outline

Image Transcriptionclose

Two infinite grounded parallel conducting planes are separated by a distance d. A point charge q is placed between the planes. Use Green's reciprocation theorem to prove that the total induced charge on one of the planes is equal to -q times the fractional perpendicular distance of the point charge from the other plane. (Hint: As your comparison electrostatic problem with the same surfaces choose one |whose charge densities and potential are known and simple.)

fullscreen
check_circleAnswer
Step 1

Write the Green’s reciprocation theorem as follows:

dx'da= , p«Dd°x + [ o{Dda
(1)
Here
p is the volume charge density,
V is the volume bounded,
S is the conducting surface area
Dis the potential due to volume charge density,
o is the surface charge density,
Dis the potential due to another charge distribution, and
p', o' are another charge distribution parameters
help_outline

Image Transcriptionclose

dx'da= , p«Dd°x + [ o{Dda (1) Here p is the volume charge density, V is the volume bounded, S is the conducting surface area Dis the potential due to volume charge density, o is the surface charge density, Dis the potential due to another charge distribution, and p', o' are another charge distribution parameters

fullscreen
Step 2
and the point charge at
2
Consider top plane at z =
bottom plane at z = --
2
(-0y-02-)
d
x 0, y 0, z
a
Here, a is the distance between the top plane and the point charge.
Consider that, there is no charge density inside the volume. Therefore, p' = 0
Consider that, there is a uniform charge +o
on the lower plane and a uniform charge
on the upper plane.
0
help_outline

Image Transcriptionclose

and the point charge at 2 Consider top plane at z = bottom plane at z = -- 2 (-0y-02-) d x 0, y 0, z a Here, a is the distance between the top plane and the point charge. Consider that, there is no charge density inside the volume. Therefore, p' = 0 Consider that, there is a uniform charge +o on the lower plane and a uniform charge on the upper plane. 0

fullscreen
Step 3

Use the symmetrical property, physical considerations, and write the electr...

E i
E0
E-V
help_outline

Image Transcriptionclose

E i E0 E-V

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Our solutions are written by experts, many with advanced degrees, and available 24/7

See Solution
Tagged in

Engineering

Electrical Engineering

Related Electrical Engineering Q&A

Find answers to questions asked by student like you

Show more Q&A add
question_answer

Q: The circuit in the attached image has voltage gain |VL|/|Vi|=170 What is the voltage gain |VL|/|Vi| ...

A: The voltage gain for given circuit needs to be determined.

question_answer

Q: What is current

A: Current: It is defined as the flow of negative charge carriers (electrons) from one region to anothe...

question_answer

Q: If 31.25 × 1018 electrons are removed from a neutral dielectric, how much charge is stored in coulom...

A: Write the expression for charge stored in terms of coulombs as follows:

question_answer

Q: A charge of 0.05 C moves past a given point every 0.1 s. How much is the current?

A: If Q is the charge in coulomb (C), t is the time in seconds (s) and I is the current in amperes (A) ...

question_answer

Q: How do you calculate the resistance value in ohms for the conductance value of 0.001 S?

A: Resistance R and conductance G are related according to the following formula:

question_answer

Q: Also show that the power balance is achieved.

A: Mark the node by their voltages as shown below-

question_answer

Q: 12- Find i(t) and v(t) in the following circuit. You may employ any method you wish. 24"φ

A: When t < 0, the inductor acts as a short circuit.So, at time t=0, we will get :

question_answer

Q: A 230-kV, three-phase transmission line has a per phase series impedance of .... (please see attache...

A: We only answer the first three parts of a question on this platform, unless specified otherwise. Sin...

question_answer

Q: A single phase overhead transmission line delivers 4000 kW at 11 kV at 0·8 p.f. lagging. If resistan...

A: The equivalent circuit diagram is as follows:

Sorry about that. What wasn’t helpful?