Is the Equilibrium of the Negative Charge at Point A Stable or Unstable?

[Saitama]

Homework Statement

A negative charge placed at point A is

a)in stable equilibrium along x-axis
b)in unstable equilibrium along y-axis
c)in stable equilibrium along y-axis
d)in unstable equilibrium along x-axis
(There can be more than one answers)

Homework Equations

The Attempt at a Solution

The particle is in equilibrium since the net force is zero. But the question asks whether the equilibrium is stable or unstable? I don't get it what the question means by that. What are the criteria for checking whether the equilibrium is stable or unstable?

 

[Infinitum]

Do you know stable and unstable equilibrium?

To check for which kind of equilibrium it is, think of what would happen if you displace the object very slightly in the direction you need to check, then depending on the behavior after the displacement, you can say whether it is a stable or unstable equilibrium.

 

[Saitama]

Do you know stable and unstable equilibrium?

To check for which kind of equilibrium it is, think of what would happen if you displace the object very slightly in the direction you need to check, then depending on the behavior after the displacement, you can say whether it is a stable or unstable equilibrium.

About stable equilibrium, i only that the potential energy should be minimum otherwise its an unstable equilibrium. But i have never ever been able to utilize this fact to solve the questions.

If i displace the negative charge in vertical direction, it will tend to return to the original position as the net force is in downward direction. But how will that help me to check whether it is in stable equilibrium?

 

[Infinitum]

About stable equilibrium, i only that the potential energy should be minimum otherwise its an unstable equilibrium. But i have never ever been able to utilize this fact to solve the questions.

Here is a very basic guide to understand equilibrium http://www.citycollegiate.com/staticsXb.htm

Stable equilibrium is one in which the body comes back to its original position when displaced slightly, unstable is the opposite and the body never attains its original position. Neutral is something in between. Here, it neither tries to get back its original position nor tries to change its configuration after the displacement.

If i displace the negative charge in vertical direction, it will tend to return to the original position as the net force is in downward direction. But how will that help me to check whether it is in stable equilibrium?

Can you answer this now?

 

[Saitama]

Can you answer this now?

Then it must be in stable equilibrium along y-axis, But what about x-axis? I can't build up the scenario.

 

[Infinitum]

Then it must be in stable equilibrium along y-axis, But what about x-axis? I can't build up the scenario.

Yep, for y-axis

For x axis, how would the forces act if you move it to the right a wee bit? What kind of motion would it undergo, then?

 

[Saitama]

Yep, for y-axis

For x axis, how would the forces act if you move it to the right a wee bit? What kind of motion would it undergo, then?

It should perform SHM, right?

 

[Infinitum]

It should perform SHM, right?

Um, nope.

Which of the forces is greater, the one due to the right or due to the left?? Which way would the particle move then??

 

[Saitama]

Um, nope.

Which of the forces is greater, the one due to the right or due to the left?? Which way would the particle move then??

The force due to the right particle is greater.
Oops, i should have seen the opposite nature of charges before answering that it should perform SHM.
Then its unstable along x-axis.

Thanks for the help Infinitum!