Earthing the plates (one or both) of a parallel plate capacitor — How can one make use of the fact that the potential of the plate is zero?
Please take a look at this question :
I'm having trouble uploading the picture. Please use this Google Drive link for now to see the diagram.
In Fig. 4.97, plate $A$ has $100 * 10^{-6}$ C charge, while plate $B$ has $60 * 10^{-6}$ C charge. Find the values of $q_{1}, q_{2}, q_{3}, q_{4}$ when
1. Both switches are open (no doubts here)
2. Only switch $S_{1}$ is closed
3. Switch $S_{2}$ is also closed / both switches are open
(Please see the Google Drive link mentioned above for the diagram)
The answers provided are (all values in $10^{-6}$ C)
1. (This one is easy) $q_1 = 80, q_2 = 20, q_3 = -20, q_4 = 80$
2. (This one is a doubt) $q_1 = 0, q_2 = -60, q_3 = 60, q_4 = 0$
3. (This one is also a doubt) $q_1 = q_2 = q_3 = q_4 = 0$
My approach for such problems
Basically, there are three things at work here.
1. <PERSON>'s law helps us to show that the charges on the inner/facing surfaces (2 & 3) will be equal in magnitude and opposite in sign.
2. 903
We know that the electric field inside the plate (assuming that it has some thickness), a conductor, is zero under electrostatic conditions. This helps us to show that the charge on the outer surface of a plate will be equal to the algebraic sum of the rest of the charges, irrespective of whether or not the plate is earthed.
3. Thirdly, and finally, when a plate is earthed, its potential becomes zero.
I know that the third point is an important clue to solve such problems, but I'm having trouble making use of this clue.
Also, notice the pattern in the answers key — whenever a plate is earthed, the charge on its outer surface becomes zero — I've seen this in <PERSON> problems. Why is this so? I know that in colloquial language, it is easy to say that the earth just neutralises the excess charge on the outer surface of the plate. But, I can't understand it terms of something concrete, like <PERSON>'s law. Also, if this is indeed the case, why wouldn't the earth neutralise all of the charge on the plate?
Update — The link wasn't working because it was private. My bad. I've turned on link sharing now.
PS : I have seen many questions here getting closed because they were specific to a certain problem and would not help future users. However, I think that my question can help one learn about the potential of a capacitor or plate. Besides, this question is not unique; many similar questions exist where one or two of the plates of a capacitor are earthed. So, I hope that the community will try to help me instead of closing my question. Thanks. 903