Continued from previous homework: A thin plastic rod of length L has a positive charge Q uniformly distributed along its length. L- (a' the electric field at point P, a distance y above the center of the rod when the rod is uniformly distributed. (Leave your answer in terms of L, y, and Q as unknowns for now.) Make sure you: Draw a good diagram with a sample slice of source and its field shown, write Coulomb’s law for the magnitude of the contribution to the field, dE, due to that slice, find the components, determine the appropriate integration limits, and evaluate the integrals that are not zero. If you can tell an integral is zero, you do need to say how you know but you don't need to evaluate it explicitly. find an expression for (b) At distances y much greater than the length L of the rod, we can no longer clearly discern the shape of the rod, and instead the charge distribution will look more and more like a point charge Q. Thus, if y > L we expect the expression for the electric field created by the rod at that distance to turn into the expression for the electric field created by a point charge Q at a distance d from the test point. Check this prediction in two ways: by explicitly evaluating the expression you got in part a in the limit y » L and by calculating the numerical ratio of the exact (from part a) and approximate (treating al the charge as a point source) expressions when L = 0.0001y. Note: We are not looking for the strict mathematical limit of infinitely large y (for which E = 0), but rather for an expression that describes the dependence of E on y when y » L. (c) Evaluate your answer to part a (the field due to the charge distributed uniformly charge) for L = 3.0m and y = 0.5m and compare to our answer from (where we had the same
Continued from previous homework: A thin plastic rod of length L has a positive charge Q uniformly distributed along its length. L- (a' the electric field at point P, a distance y above the center of the rod when the rod is uniformly distributed. (Leave your answer in terms of L, y, and Q as unknowns for now.) Make sure you: Draw a good diagram with a sample slice of source and its field shown, write Coulomb’s law for the magnitude of the contribution to the field, dE, due to that slice, find the components, determine the appropriate integration limits, and evaluate the integrals that are not zero. If you can tell an integral is zero, you do need to say how you know but you don't need to evaluate it explicitly. find an expression for (b) At distances y much greater than the length L of the rod, we can no longer clearly discern the shape of the rod, and instead the charge distribution will look more and more like a point charge Q. Thus, if y > L we expect the expression for the electric field created by the rod at that distance to turn into the expression for the electric field created by a point charge Q at a distance d from the test point. Check this prediction in two ways: by explicitly evaluating the expression you got in part a in the limit y » L and by calculating the numerical ratio of the exact (from part a) and approximate (treating al the charge as a point source) expressions when L = 0.0001y. Note: We are not looking for the strict mathematical limit of infinitely large y (for which E = 0), but rather for an expression that describes the dependence of E on y when y » L. (c) Evaluate your answer to part a (the field due to the charge distributed uniformly charge) for L = 3.0m and y = 0.5m and compare to our answer from (where we had the same
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Answer all parts (a,b,c) of the physics problem. thanks!
Transcribed Image Text:Continued from previous homework: A thin plastic rod of length L has a positive charge Q uniformly
distributed along its length.
L
(a'
the electric field at point P, a distance y above the center of the rod when the rod is uniformly
distributed. (Leave your answer in terms of L, y, and Q as unknowns for now.) Make sure you:
Draw a good diagram with a sample slice of source and its field shown, write Coulomb's law
for the magnitude of the contribution to the field, dE, due to that slice, find the components,
determine the appropriate integration limits, and evaluate the integrals that are not zero. If you
can tell an integral is zero, you do need to say how you know but you don't need to evaluate it
explicitly.
find an expression for
(b) At distances y much greater than the length L of the rod, we can no longer clearly discern
the shape of the rod, and instead the charge distribution will look more and more like a point
charge Q. Thus, if y > L we expect the expression for the electric field created by the rod at
that distance to turn into the expression for the electric field created by a point charge Q at a
distance d from the test point.
Check this prediction in two ways: by explicitly evaluating the expression you got in part a in the
limit y > L and by calculating the numerical ratio of the exact (from part a) and approximate
(treating al the charge as a point source) expressions when L = 0.0001y. Note: We are not
looking for the strict mathematical limit of infinitely large y (for which E = 0), but rather for
an expression that describes the dependence of E on y when y > L.
(c) Evaluate your answer to part a (the field due to the charge distributed uniformly charge) for
L = 3.0m and y = 0.5m and compare to our answer from
(where we had the same
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