Understanding Electric Fields and Capacitance for Suspended Charged Disk

In summary, the conversation discusses a problem involving a uniform charged disk suspended above an infinite conducting plane and the calculation of the electric field vector, capacitance, and energy formulas for the system. The electric field formula for a disk is also provided, along with a picture and a question about the direction of the electric fields. The conversation concludes with a request for assistance and a clarification about reversing the direction of the unit vector for the electric field.
  • #1
brad sue
281
0
HI I don't understand the method of image.
I have this problem:

A uniform charged disk is suspended ( at a distance h) above an infinite conducting plane ( disk is parallel to the plane). The disk carries a charge Q and has a diameter d. Assume d>>h.
1- Calculate the electric field vector near the center and below the disk.
2- Calculate the capacitance of the system using the formula C=Q/V.
3- Calculate the capacitance of the system using the energy formulas.


I attach a picture.
I get lost at some point

the electric fiel for a disk is:
E=Qy/(2*pi*epsilon)*(1/y-1/(sqrt(y^2+R^2)) y (unit vector)

to answer the question 1-:
electric field from charge Q:
EQ=Q(h-y)/(2*pi*epsilon)*(1/(h-y)-1/(sqrt((h-y)^2+R^2)) (-y) (unit vector)

electric field from charge -Q ( the image):
E-Q=-Q(h+y)/(2*pi*epsilon)*(1/(h+y)-1/(sqrt((h+y)^2+R^2)) (-y) (unit vector)

Here is my first problem: the direction of the two electric fields EQ and E-Q.
I am not sure about the electric field of the expressions.

(I suspect I get some mistakes because I tried a similar problem but with a more simple expression for the 2 fields and when I add them, I get zero)

I would really have some help with this problem.

please can someone help me?
Thank you
 

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  • #2
Reverse the direction of the unit vector y for [tex]E_{-Q}[/tex] because the polarity is opposite to [tex]E_{Q}[/tex].
 
  • #3
thanks.
I will try to continue from there.
 

FAQ: Understanding Electric Fields and Capacitance for Suspended Charged Disk

What is the image method in science?

The image method in science is a mathematical technique used to solve a variety of problems related to electrostatics, fluid dynamics, and other physical phenomena. It involves creating a mirror image of an object or source and using that image to simplify calculations and understand the behavior of a system.

How does the image method work?

The image method works by creating a mirror image of an object or source in a system, and then using that image to simplify calculations and understand the behavior of the system. This allows scientists to use known solutions to similar problems to solve more complex problems.

What are some applications of the image method?

The image method has a wide range of applications in science, including calculating electric fields and potentials in conductors and dielectrics, determining the force on a charged particle in an electric field, and understanding the flow of fluids around obstacles in a fluid dynamic system.

What are the limitations of the image method?

The image method has some limitations, such as only being applicable to certain types of problems and systems. It also assumes idealized conditions, such as infinite conductors or perfect fluids, which may not always be the case in real-world situations. Additionally, the image method can become more complex and difficult to use in more complex systems.

How is the image method different from other mathematical techniques?

The image method differs from other mathematical techniques in that it relies on creating a mirror image of an object or source in a system, rather than directly solving equations or using numerical methods. It is also specifically designed for problems in electrostatics and fluid dynamics, while other techniques may have broader applications in science and mathematics.

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