electric field of a stick A stick with length l has charge Q uniformly distribut
ID: 1767757 • Letter: E
Question
electric field of a stick
A stick with length l has charge Q uniformly distributed on it. It lies along the x axis between the points x = -l and x = 0. A point charge also with charge Q lies on the x axis at the point x = t. Let x = a be the point on the x axis between the two objects where the electric field is zero. Find a. There happens to be one other point where the electric field is zero (it's inside the stick). In addition to this one, are there any other points in space where the electric field is zero? Why or why not? Make a rough sketch of the field lines and equipotential curves everywhere in the plane of the paper. Be sure to indicate how the lines and curves make the transition from their shapes close to the objects to their shapes far from them. (Don't worry about what's going 011 extremely close to the stick.) What do things look like near the point you found in part (a)?Explanation / Answer
a)
k Q/(L - a)^2 = k Q/(a (L + a))
==> 1/(L - a)^2 = 1/(a (L + a))
==> (L - a)^2 = a (L + a)
==> L^2 + a^2 - 2 a L = a L + a^2
==> L^2 - 3 a L = 0
==> a = L/3
b)
Yes, in 3 dimention there is infinity number of points with E=0.
c)
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