Two point charges, 3.4 C and -2.0 C , are placed 5.0 cm apart on the x axis. Ass

Question

Two point charges, 3.4 C and -2.0 C , are placed 5.0 cm apart on the x axis. Assume that the negative charge is at the origin, and the positive x-axis is directed from the negative charge to the positive. Part A)

At what points along the x axis is the electric field zero.

Express your answer using two significant figures. If there is more than one answer, give your answers separated by commas.

Part B) At what points along the x axis is the potential zero? Let V=0 at r=.

Express your answer using two significant figures. If there is more than one answer, give your answers separated by commas.

Explanation / Answer

SOLUTION:

Left and right are meaningless unless the relative locations of q1 and q2 are given, which they aren't. So I'll just give distance from q2 and state whether that's "inside" (between q1 and q2) or "outside" (beyond q2)

A. One null-field point at 0.12753 m, outside.
[ Derivation: (d2/d1)^2 = -q2/q1 ==> d2/d1 = -sqrt(|q2/q1|) ==>
R/d1 = 1-sqrt(|q2/q1|) ==> d1 = R/(1-sqrt(|q2/q1|)) ]
B. Two null-voltage points.
One at 0.00706 m, inside.
[ Derivation: V = k(q1/d1+q2/d2) = 0 ==> d1/d2 = -q1/q2;
define R = x2-x1 = d1+d2 ==> 1 = R/(d1+d2) ==> d2 = R/(d1/d2+1) ]
One at 0.06 m, outside
[ Derivation: Same as above, except R = x2-x1 = |d1-d2| ==> d2 = -R/(d1/d2-1) ]

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