# Find the electric field

Delta2
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But, actually your approximation doesn't match with any option. What should I do next (with this equation)?
Could be that my equations are wrong. Can you tell me what are the available options, maybe i can do some reverse engineering of some sort ...

Could be that my equations are wrong. Can you tell me what are the available options, maybe i can do some reverse engineering of some sort ...
Look at this picture..
1.

$$\frac{1}{2} kx^2 + \frac{1}{2} ky^2 - qEY$$

2.

$$\frac{1}{2} kx^2 + \frac{1}{2} ky^2 - qE(Y+X) + \frac{1}{2} K''(L-x-y)^2$$

3.

$$\frac{1}{2}kx^2+\frac{1}{2}ky^2-qEY+\frac{1}{2} (L-x-y)^2$$

4.

$$\frac{1}{2}kx^2+\frac{1}{2}ky^2-qE(x+y)$$

5.

$$\frac{1}{2}kx^2+\frac{1}{2}ky^2+\frac{1}{2}k''(L-x-y)^2$$

Unfortunately, MathJax isn't working. I had tried with "####" also. I had tried as we use in SE or, CD

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Delta2
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Ehm I don't think these options are candidates to the equilibrium position , they are rather candidates for the total potential energy of the system. Try option 2 and tell me if it is correct.

Steve4Physics
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As I mentioned in my previous reply that this question is not mine. It's another person's. I didn't have much more time to look at his works. So, that what I simply understood without reading answer and question, I had just added that. As I said I didn't have much more time, that's why I added unnecessary **Homework Statement**
My apologies. You are just trying to help someone out. Well done for that!

But note, even after 28 posts, we do not know what the actual question is! If at all possible, post the complete question. We shouldn't have to make any assumptions such as "the springs have zero natural length" (@Delta , Post #23); all essential information should be included as part of the question.

Delta2
Ehm I don't think these options are candidates to the equilibrium position , they are rather candidates for the total potential energy of the system. Try option 2 and tell me if it is correct.
Actually, that was like an exam (Olympiad). My friend had joined to that. Then, he thought his work isn't correct that's why he told me to post it here.

And, no matter what I choose the site won't show correct answer. That's why I/he wants to know the approximation/answer.

My apologies. You are just trying to help someone out. Well done for that!

But note, even after 28 posts, we do not know what the actual question is! If at all possible, post the complete question. We shouldn't have to make any assumptions such as "the springs have zero natural length" (@Delta , Post #23); all essential information should be included as part of the question.
Actually, I had gave the whole question and, figure in following picture. You can see the whole question in the image also.

Delta2
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Actually, I had gave the whole question and, figure in following picture. You can see the whole question in the image also.
Actually I cant see what the question is. I can read only the description of the system. What I can guess is asking (judging from the available options) is "What is the total potential energy of the system?"

Steve4Physics
Actually I cant see what the question is. I can read only the description of the system. What I can guess is asking (judging from the available options) is "What is the total potential energy of the system?"
Yes! You got the question..

Delta2
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Yes! You got the question..
The correct option according to my opinion is option 2.

Steve4Physics
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And, no matter what I choose the site won't show correct answer.
I'm not surprised!

@Delta has (I believe correctly) guessed that the question is 'What is the potential energy?'. But original question does not even mention potential energy!

The meaning of distances X and Y is very unclear. The question-wording does not mention X or Y. And the diagram in Post#1 does not show X and Y properly. (An accurate diagram showing the meanings of X and Y would help a lot.)

Assuming you have posted the full question, then it seems that whoever wrote the original question made a lot of bad mistakes/omissions. Without guesses/assumptions, the question is unanswerable.

Delta2
I'm not surprised!

@Delta has (I believe correctly) guessed that the question is 'What is the potential energy?'. But original question does not even mention potential energy!

The meaning of distances X and Y is very unclear. The question-wording does not mention X or Y. And the diagram in Post#1 does not show X and Y properly. (An accurate diagram showing the meanings of X and Y would help a lot.)

Assuming you have posted the full question, then it seems that whoever wrote the original question made a lot of bad mistakes/omissions. Without guesses/assumptions, the question is unanswerable.
Yes! That's true. I couldn't understand the question either. But, when I looked at option it was showing like they want us to find Potential Energy...

Delta2
kuruman
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The correct option according to my opinion is option 2.
I agree with your opinion and I also agree that the problem could have been stated better. This is what I think is the case. We start in zero electric field with the masses at equilibrium and the springs unstretched. Now we turn the field ON. Say the charged mass experiences an electric force to the right. Both masses will move to the right and we have the new equilibrium configuration as shown in the picture. The key question is how to interpret X and Y. The only interpretation that makes sense in view of the answers is that they represent the extra amount by which each spring is stretched as the charged mass moves to the right. Then one must add up the potential energy changes of the three springs plus the change in electric potential energy.

Istiakshovon, Steve4Physics and Delta2
Steve4Physics
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... We start in zero electric field with the masses at equilibrium and the springs unstretched. Now we turn the field ON. Say the charged mass experiences an electric force to the right. Both masses will move to the right and we have the new equilibrium configuration as shown in the picture. The key question is how to interpret X and Y. The only interpretation that makes sense in view of the answers is that they represent the extra amount by which each spring is stretched as the charged mass moves to the right. Then one must add up the potential energy changes of the three springs plus the change in electric potential energy.
That sounds like the intention of the question's original author.

But the spring on the right gets compressed by an amount X+Y (the same as the distance m moves, which is independent of L). The overall potential energy change (assuming q is positive) is then:
½kX² + ½k’Y² - qE(X+Y) + ½k’’(X+Y)²

This is not in the answer-list. I guess that the answer-list is also wrong!

It may be worth noting that (assuming no losses)
½kX² + ½k’Y² - qE(X+Y) + ½k’’(X+Y)² = 0
because
work done by electric field = gain in elastic potential energy.
or equivalently
loss of electrical potential energy = gain in elastic potential energy.

Istiakshovon and kuruman
kuruman
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That sounds like the intention of the question's original author.

But the spring on the right gets compressed by an amount X+Y (the same as the distance m moves, which is independent of L). The overall potential energy change (assuming q is positive) is then:
½kX² + ½k’Y² - qE(X+Y) + ½k’’(X+Y)²

This is not in the answer-list. I guess that the answer-list is also wrong!

It may be worth noting that (assuming no losses)
½kX² + ½k’Y² - qE(X+Y) + ½k’’(X+Y)² = 0
because
work done by electric field = gain in elastic potential energy.
or equivalently
loss of electrical potential energy = gain in elastic potential energy.
You are absolutely correct, good catch. I derived the same expression but didn't notice the difference between my expression and theirs. It seems that the question's author had one X & Y definition for the first two springs and another for the third spring.

Istiakshovon and Steve4Physics