Using Intuition to Solve Problems like this:

[ilovemcat]

I'm trying to use my intuition to solve problems like this but I'm having trouble with it. So here's the question:

Two charges, +3Q and -Q, are fixed at a distance d to the left and right of the origin along the x axis as shown above (they include some graph with a distance labeled "d" pointing left and right from origin --> total distance = 2d). The potential infinitely far from the charges shown is equal to zero. Find the position on the x axis CLOSEST TO THE ORIGIN where the potential is also zero.

Now I know there's a very math heavy approach for this, but I would much rather use my intuition to solve this problem. Please tell me if my logic sounds right. Warning: This might be difficult to follow.

The point at where they equal zero is when the potential for both charges are equal in magnitude. So first, I realize that the charge on (3Q) vs. (-Q) is 3 times greater. That alone would make the potential 3x greater at some distance "r". In order for the potential (for Q) at some distance "r" to be equal in magnitude to (3Q), point "r" would have to be 3 times closer to (-Q) than to (-3Q) to make the potential 3x at (-Q) 3x greater and therefore equal to the potential at (-3Q).

So... a distance 3x closer is the same thing as a ratio of 1:3. As a fraction, this ratio equals 1/4 of the total distance. Therefore, if the total distance is "2d" then 1/4 of the total distance is 2d/4 or d/2. This is the distance relative to the -Q charge and is also point where the potential is zero.

Now here are the choices:

A. d/4 to the left of the origin
B. d/2 to the left of the origin
C. d/4 to the right of the origin
D. d/2 to the right of the origin

The answer is D. This problem is a total mind f**k. Anyone else have trouble solving problems like this? Should I just stick to the calculation approach instead? o_o

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[PiBond]

I first eliminate A and B because the potential won't be zero on the left side of the origin. It'll be zero a point near the smaller charge since we know that the overall potential is just the sum of the individual potentials (and here we've got opposite charges). I pick D because we're 3 times closer to the smaller charge than the larger one.

Sorry if that was too terse but that's honestly how I would answer that question.

 

[ilovemcat]

I first eliminate A and B because the potential won't be zero on the left side of the origin. It'll be zero a point near the smaller charge since we know that the overall potential is just the sum of the individual potentials (and here we've got opposite charges). I pick D because we're 3 times closer to the smaller charge than the larger one.

Sorry if that was too terse but that's honestly how I would answer that question.

I feel like an idiot now. Thanks. The MCAT's gonnna screw me overrrrrr

 

[cartman1980]

I feel like an idiot now. Thanks. The MCAT's gonnna screw me overrrrrr

You aren't the only one to feel that way
I looked at the problem and came to the wrong conclusion as well. My logic was that + will attract negative (similar to proton-electron behaviour). Therefore, the - charge will move closer to the + charge until a point of no return. At this point, the net potential should be zero. And being that 3x magnitude of attraction is being generated by -3Q, zero potential should exist to the left side of the origin.