Consider four point charges placed at the corners of a square of side s = 0.5 μm. Two charges, diagonally opposite each other, are +0.7 nC. Another of the charges is -12 nC. a) What will be the electric potential at the center of the square if the fourth charge is -6 nC (assume the conventional zero point definition for each individual charge throughout this problem)? b) What should the fourth charge be, if the electric potential is to be zero at the center? Draw the configuration (multiple orientations are possible, any correct one is acceptable). c)Is it fair to say the electric field must now be zero at this point because the electric potential is? Why or why not?
Consider four point charges placed at the corners of a square of side
s = 0.5 μm. Two charges, diagonally opposite each other, are +0.7 nC.
Another of the charges is -12 nC.
a) What will be the electric potential at the center of the square if the
fourth charge is -6 nC (assume the conventional zero point definition for
each individual charge throughout this problem)?
b) What should the fourth charge be, if the electric potential is to be zero
at the center? Draw the configuration (multiple orientations are possible,
any correct one is acceptable).
c)Is it fair to say the electric field must now be zero at this point because
the electric potential is? Why or why not? What condition must be met to
conclude that the electric field is zero there?
d) The fourth charge and the -12 nC charge are now removed, so we have
just the two +0.7 nC charges. Is the electric potential now zero at the center
of the square? What is its value?
Define a coordinate (x, y, z or whatever you want) axis that points from
one of the charges to the other. Put the origin at the center. Neatly, plot
the total electric potential as a function of this coordinate along that axis.
Determine from your graph alone is the electric field zero at any point on
the axis? If so where? Why or why not? Does your answer make sense from
the perspective of superposition of electric fields? Does your answer make
sense from a symmetry perspective?
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