lmao asked in Science & MathematicsPhysics · 2 months ago

Two point charges, Q1 = 3.2 μC and Q2 = -1.3 μC , are placed on the x axis. Suppose that Q2 is placed at the origin, and Q1 is placed at the coordinate x1 = − 4.0 cm (Figure 1).

A) At what point(s) along the x axis is the electric field zero? Determine the x-coordinate(s) of the point(s).

B) At what point(s) along the x axis is the potential zero? Determine the x-coordinate(s) of the point(s). (!!!!!2 coordinates please!!!!)

Relevance
• NCS
Lv 7
1 month ago

A) field E = vector Σ kQ / d²

Since the two charges have opposite sign, there is ONE point where the field is zero, and it lies OUTSIDE of the two charges and close to the one with smaller magnitude. So we need the point where

k*3.2µC/(4.0cm + x)² = k*1.3µC/x²

3.2x² = 1.3(4 + x)²

for x in cm.

x = -1.6 cm ← ignore negative root

and x = 7.0 cm ◄

B) potential U = algebraic Σ kQ / d

There can't be a point to the left of Q1 where this is true.

If there is a point between the two charges, then

k*3.2µC / (4.0cm - x) = k*1.3µC / x

3.2x = 1.3(4 - x)

for x in cm.

This has a solution at x = 1.16 cm, which puts the point at

X = -1.16 cm ≈ -1.2 cm

to two significant digits.

If there is a point to the right of Q2, then

k*3.2µC / (4.0cm + x) = k*1.3µC / x

3.2x = 1.3(4.0 + x)

This has a solution at

x = 2.7 cm

for a total of two such points.