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charges and fields
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"\nThe field at location C can be described as \n\n", | |
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" is the distance between the proton and point C. Given the magnitude of the \ | |
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" is facing north, the location of the proton is south relative to point C.\n\ | |
Thus, we see that the proton must be placed south of point C, ", | |
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StyleBox["Due to the negative charges on the surface of the plastic disk, \ | |
the free negative charges in the foil will move away from the disk in the \ | |
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surfaces and should be evenly distributed, as the image above.", | |
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StyleBox["(b)\n", | |
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StyleBox["Point x at the center of the foil is inside the foil, which is a \ | |
conductor, so the net electric field is 0 at that point. This is because the \ | |
free charges in the aluminium foil will move due to the electric field \ | |
produced by the plastic disk in a way that cancels it out. As long as there \ | |
is still electric field inside the foil, there are more charges to move \ | |
because charges are moved by the presence of an electric field. I assume here \ | |
that there is abundant free charge in the aluminium foil to cancel out the \ | |
electric field created by the plastic disk.\n", | |
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"\nWe can consider the electric field created by the plastic disk at the \ | |
point x from part (b) and the electric field at the same point created by the \ | |
left-side surface charges on the foil.\nSince ", | |
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", we can say that the electric field created by the plastic disk is\n", | |
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"\nHere, the coordinate is taken so that positive values indicate rightward \ | |
(in the direction from the disk to the foil) and negative values indicates \ | |
leftward.\nSince at point x, the net electric field is 0, we can deduce that \ | |
the surface charges on the foil create an electric field of \n\n", | |
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"\nWhere ", | |
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" is the total positive charge on the left side surface of the foil. It is \ | |
divided by two because the canceling field is created equally by the right \ | |
side and the left side surface, while we are only interested in the right \ | |
side.\n \nNow, equate the two equations above and we see that\n\n", | |
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StyleBox["Chao\[CloseCurlyQuote]s suggested problem\n", | |
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"From the textbook, you learned how to find the electric field above a \ | |
circular loop of charge. What about the electric field x meters above the \ | |
center of a square loop of side length b meters? The square loop has total \ | |
charge Q and is uniformly distributed along the loop.\nI will address the \ | |
target point as A in this question. \nWe can combine the effects of 4 \ | |
different charged straight rods. Per rod, we can use the equation:\n\n", | |
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