Two positive point charges q1 and q2 are separated by a distance d.

[Joa Boaz]

Two positive charges Q1 and Q2 are separated by a distance d. Find a general expression for the distance from Q1 at which the electric field is 0 by defining Q2 as alphaQ1 (alpha > 0 with alpha not equal to 1). This expression should contain alpha, d, and possible some numeric constants. Check that your expression makes sense by setting Q2 = 4Q1

I have attached the problem and what I have worked out.

This is what I have, but unsure about it

 

[Orodruin]

In your first expression for the field, you have only added the magnitude of the fields from the different charges. Then in the second line you have changed the sign of one of the charges (which is what it should be - between the charges the fields act in different directions).

Finally you should solve for x (which should be trivial given you have $d = x(1+\sqrt\alpha)$. Apart from that, I am not sure what you are really asking. You should also argue why your result for the check is reasonable.

 

[Joa Boaz]

Thank you.

I am just trying to see whether I am going about solving the above problem correctly. Am I taking the right path? I find physics confusion, I guess, it doesn't help that most of the time my instructor is merely doing the same exactly example that the author provides step by step in the textbook. I am just trying to understand physics 2.

 

[Orodruin]

The mathematics of your first post were correct apart from the first row. Since you should be in between the charges, x shoud be between 0 and d - so your result from there was correct. The only thing I was critisising was the first row which looked strange and did not explain the minus sign you introduced in the second.

 

[Joa Boaz]

Oh, I see, I am sorry, I didn't understand your comment. I thought you said that my whole equation was wrong. The reason I have a negative it is because Q1 and Q2 are both positive and if I have up and right as my positive. This seems to suggest that Q1 electric field are moving away or to the left which means it is negative. At least, that was my take of this problem. But, I wouldn't be surprise to see that I am complete wrong.

 

[Orodruin]

No, your reasoning is the correct one. However, this should have showed up as a a minus sign already in the first line.

 

[Joa Boaz]

I see. Thank you.