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Problem
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Electromagnetism$\Rightarrow$}Conductors

A conductor has the magical mystical property of inducing the exact opposite charge of a nearby charge. One has all the electrons in the conductor moving towards the positive charge placed outside Q. A net negative charge of -Q is induced.

(Also, one recalls that this was the assumption made in finding the potential of this setup using the Method of Images---the charged plane was assumed to have a charge density $-Q/A$.)

Alternate Solutions
 sonnb2009-01-27 20:29:35 The question should read "What is the total charge induced on the top face of the plane". Otherwise, there should be an induced charge on the bottom face of the plane of +Q. Then the answer should be (C).Reply to this comment
gmeheretu
2012-05-07 14:24:09
By the method of images, the induced charged would be -Q.
phoxdie
2010-11-12 21:21:03
Just to point something out which may be easy to remember in case the image charge is confusing or you forget it. Consider the case where no charge +Q is present, and we only have the GROUNDED conducting plane. If you were to draw the initial charge with '+' and '-' signs they would be evenly placed across the plane. When we introduce the charge +Q, this repels the '+' charge on the plane, you can think of it as 'pushing' positive surface charges into ground, or as pulling negative charge from the ground to the surface of the plane. This at least tells you the plane is now negative, and it doesn't make sense that it should have a charge twice as much so D is a safe answer.
wittensdog
2009-10-08 19:10:38
Note very carefully that the plane needs to be GROUNDED. If it is not grounded, there is no source of charge that the plane can draw from in order to gain a net charge. This fact is used in the method of images, since we require the plane to go to zero potential.

However, even if the plane is insulated, it could still have its charge move around and gain a surface charge. But the net charge on the plane would not be able to change from zero.

If the plane is held at some non-zero potential, then it gets more complicated.
sonnb
2009-01-27 20:29:35
The question should read "What is the total charge induced on the top face of the plane". Otherwise, there should be an induced charge on the bottom face of the plane of +Q. Then the answer should be (C).
 jmason862009-07-14 19:51:49 My EM is a little rusty, but I think that the +Q charge that is induced on the bottom half gets dumped by way of the grounding that the problem states.
 beradg072010-07-11 02:59:05 But the plane is a 2 dimensional object so there is no such thing as a top and bottom face, they are the same face. Thus the question is correct as stated.
 tachyonicbrane2012-11-09 16:57:06 But the fact that it's grounded means that it's connected to a charge bath. (Grounded for electrical conductors is like being in a heat bath for thermal conductors.)
 epuma2013-10-15 19:32:22 This problem deals with the concept electrostatic induction. The ground is the key. Because the conductor is grounded, the positive charges are essentially whisked away, leaving behind a plane of charge -Q. (If the movement of positive charge is unsettling, you could similarly argue that the grounded plane draws from an infinite pool of negative charges to neutralize the positive charges on the bottom half.) If the plate were not grounded, you would be correct in saying that the answer should be (C). But in this case, the answer is unequivocally (D).
 skeptical2014-09-24 03:20:30 True for a conductor which is not grounded. However, this is a grounded conducting plane, so the net induced charge is truly -Q.
 jdbro2014-10-24 19:47:14 Hence, grounded.
 physgre2015-10-15 02:25:52 It says grounded.
a19grey2
2008-11-05 20:32:19
So, if magic and mystery aren't your thing... (and if you're a physicist, they shouldn't be), then check out the method of image charges which explains how to do these types of problems.

http://en.wikipedia.org/wiki/Method_of_image_charges
 buaasyh2014-10-17 03:41:36 For physics, the starting point of logic are physical phenomena rather than phisical laws, which are assumed, deduced and validated by observation and analysis of physical phenomena. Thus, to say magical or mystical is not necessarily untrue. After all, who knows how it comes.That will date back to a long time ago. Anyway, there is not much point caring about it. There are many phenomena to be observed and analyzed and made assumptions about. Some of them may help find how it comes.
rajendratimilsina
2008-10-23 18:09:41
I am agree with this solution because conductor has a special property of inducing charge nearby the given charge.

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