Find Equilibrium with Electron Field on Figure 22-11

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In the discussion about finding equilibrium for an electron in relation to charged particles in Figure 22-11, participants explore the concept of net force on an electron placed at various points along an axis. A non-computational technique is suggested, involving dividing the line into regions and analyzing the direction of forces on an electron at specific points. The approach highlights that if the net force direction changes between two points, an equilibrium point must exist in that interval. The discussion emphasizes the application of Coulomb's Law to calculate forces from each charge acting on the electron, noting the need for algebra to pinpoint equilibrium locations accurately. Overall, the conversation focuses on understanding how to determine where an electron can achieve equilibrium in the presence of multiple fixed charges.
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Figure 22-11 shows four situations in which charged particles are fixed in place on an axis.

http://www.webassign.net/hrw/22_11.gif

Figure 22-11.
In which situations is there a point to the left of the particles where an electron will be in equilibrium?

Need some help, have absolutely no idea where to start.
Can be more then one answer I suppose.

thanks for any help,

RishiD
 
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Here is a non-computational technique.

Divide the line into three regions.

Choose a point in the far-left in the left region.
What is the direction of the net force on an electron placed at that point?
Intuitively, from far away, two charges in the middle are practically on top of each other. That is, we can think of them as a single point charge of size q1+q2.

Now choose a point just to the left of the left charge.
What is the direction of the net force on an electron placed at that point?
Intuitively, being so close to the left charge, the force on the electron is dominated by that left charge.
If the direction of the net force at the near-left point has changed from that of the far-left point, then there must have been a point where the net force was zero... somewhere between the far-left point and the near-left point.

If you want to locate that point exactly, you'll have to do some algebra.

(You can generalize this idea to locate equilibrium points, if any, in the center region and in the right region.)
 
robphy said:
What is the direction of the net force on an electron placed at that point?

What equation is that to find that?
 
Coulomb's Law, applied once for each charge applying a force on the electron.
 
Sorry I just cannot seem to any get any valid answers out of this...
F=(k*Q1*Q2)/r^2

r is unknown, so for example A
Q1 = +1 Q2 = -3
So wouldn't the force always be negative?
 
Think this way:
the electron is repelled by the negative charge, and
the electron is attracted by the positive charge.
At the point in question, which force is stronger?
 

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