# Limitations of the Image Method

1. Oct 5, 2007

### jamesEsnow

Hi everybody, new here. Okay, I will get straight to the chase. I am an undergrad student and I am current taking a course in electromagnetics--transmissions lines...

Anyways we just had an exam yesterday and there was a question on it that I believe may have serious flaws. I will try to explain it as well as possible without diagrams. If I can't, please let me know and I will draw up a pic and post.

So, the question stated that there were three point charges and a conducting surface on the x-y plane. Now, two of these charges will be positive and equal in magnitude: Charge 1 at (0,1,1) and Charge 2 at (0,-1,1). Here is the kicker. The third charge is located at (0,0,0) and has a positive charge of some other magnitude (can't) remember. The question asked for the force on the third charge at (0,0,0.)

By pure accident I did not see there was a conducting plane and I went ahead and used Coulombs law for the electric fied at the origin--easy stuff. On reviewing my answers I saw that a conducting plane was there. I initially thought of the method of images but it was not stated whether the conducting surface was perfect and it was NOT grounded. Furthermore, the material wasn't stated either.

Of course using image theory is easy for point charges and I understand that many problems in class are purely academic. I also understand that it would probably be reasonable to ask for an instantaneous force on the charge. In retrospect, I believe that the instructor just wanted us to use image theory anyways. However, at the time I did not use image theory and was quite confused: 1. I have never seen a problem where a charge was placed on the conducting surface in an image theory application. 2. From what I understand, the conductor must be perfect and/or grounded. 3. I have read that most metals can be approximated and material was not listed. 4. I assumed the charge will dissipate in the conductor, so it couldn't be measured with image method.

I peered further into the text and I found a section on free-charge dissipation. There was an equation that states that the charge density as a function of time equals intial charge density times e^-(σ/ε)t. Now if the conductor is perfect, then wouldn't the charge dissipate virtually instantaneously. And doesn't image method work because of "mirrored" charges moving in the conductor to counter the charge above the plane. So, it seems like by the time image method was applicable, the placed charge would have already dissapated. Therefore, the only measurement you can take is instantaneous, and this should be close to Coulomb's Law.

Now, I will cop up and accept the missed points if I was wrong, but there seems to be something wrong here. Please give me some insight. Thank You.