21.7 When charge of all these electrons! ttract. Q21.7 Figure Q21.7 shows some o

Question

21.7

When charge of all these electrons! ttract. Q21.7 Figure Q21.7 shows some of Figure 621 ys that the electric field lines due to three point pheres charges arranged along the vertical axis. All three charges have the same magni- comes tude. (a) What are the signs of the three electric charges? Explain your reasoning. (b) At harged what point(s) is the magnitude of the elec- d as in tric field the smallest? Explain your rea- still be soning. Explain how the fields produce by each individual point charge combine through to give a small net field at this point or g if all points. )than if 021.8 Good conductors of electricity, such as metak a

Explanation / Answer

(a)

Top charge - positive

Middle charge - negative

Bottom charge - positive

Positive charges have field lines originating from the, i.e. the field lines are diverging.

Negative charges are sink for the field line, i.e. field lines converge at them.

Thus, the top and bottom charges are positive while the middle charge is negative.

(b)

The magnitude of the electric field is smallest at about halfway between the middle charge and each side of the figure.

One way to visualize this is by how the field vectors add up. Each point charge produces a field vector at any point with the magnitude of the vector proportional to 1/r^2 and the direction pointiing out from positive charge and into negative charges. Look at the point to the left some distance r from the central charge. The central charge produces a field vector pointing right with magnitude 1/r^2. The top change (spaced d away) produces a vector pointing down and left of 1/(h^2 + d^2). The bottom charge produces a field of 1/(h^2 + d^2) as well but it is pointing up and left. The up and down components of the positive charge vectors exactly cancel each other leaving a left and right vector. These vectors are of similar magnitude and in opposite direction so they nearly cancel leaving only a small field. As you move away from the centerline, the amount of cancelation is less so the overall field is greater, leaving the minimum field along the center.

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