Finding a point midway between two electric charges

[Sterfrye36]

Homework Statement

Two point charges of magnitude 2nC and -4nC are separated by 35 cm. The Coulomb constant is 8.98755e9 Newtons (Meters squared/ Coulombs squared). What is the potential difference between a point infinitely far away and a point midway between the charges?

R= .175

Homework Equations

E = Kc (q/r^2)

Magnitude of electric field = Coulomb's Constant (value of the charge/ Distance squared)

Delta V = Kc (q/r)

Potential difference = Coulomb's Constant (value of the point charge)/ (distance to the point charge)

The Attempt at a Solution

I tried running the two separate charges into the first formula (E1= 587, E2= -1174), then added them together, then ran the second formula with the difference of the first two (1761) and ended up with (9.04e13).

Call me crazy, but isn't that quite a bit of voltage for such a tiny amount of charges? Where am I going wrong?

 

[anathema]

I would first confirm that the equations and values being used are correct. The magnitude of electric field formula should be E = Kc (q/r^2), not E = Kc (q/r). Also, the potential difference formula should be Delta V = Kc (q/r), not Delta V = Kc (q/r^2). Additionally, the values for the charges are given in nanocoulombs, so they should be converted to coulombs before being used in the equations.

Next, I would double check the calculations to make sure they were done correctly. Using the correct equations and values, the electric fields at the midpoint between the two charges should be E1 = 0 and E2 = -3.2e9. Adding them together gives a total electric field of -3.2e9. Then, using the potential difference formula, the potential difference between a point infinitely far away and the midpoint should be 3.2e9 volts, which is much more reasonable for the given values.

If the calculations are still not giving the expected result, I would check for any errors in the units or conversions. It may also be helpful to draw a diagram and label all the given values to ensure they are being used correctly in the equations.

Finally, I would consider the physical meaning of the result and whether it makes sense in the given scenario. A potential difference of 9.04e13 volts is extremely high and would likely lead to unexpected consequences. It is possible that the given values are not realistic or there is a mistake in the problem statement. In this case, it would be important to clarify with the person who posted the forum question.

 

[Moetasim]

I would approach this problem by first understanding the concept of potential difference. The potential difference between two points is a measure of the work needed to move a unit charge from one point to the other. In this case, we are looking for the potential difference between a point infinitely far away and a point midway between the two charges. This means that we are essentially moving a unit charge from infinity to a point midway between the two charges.

To calculate the potential difference, we can use the equation Delta V = Kc (q/r), where Kc is the Coulomb constant, q is the charge, and r is the distance between the two points. In this case, since we are moving a unit charge, q = 1. The distance r is the distance from the point midway between the charges to infinity, which is essentially the same as the distance between the two charges. So, r = 35 cm.

Plugging in the values, we get Delta V = (8.98755e9 Nm^2/C^2) * (2nC + (-4nC))/0.35m = -2.57e10 V. This is a much more reasonable value for the potential difference.

The mistake in your attempt at a solution was that you added the electric fields of the two charges, which is not the correct way to calculate the potential difference. Instead, you need to consider the work done in moving a unit charge from one point to the other, taking into account the direction and magnitude of the electric field at each point. I hope this helps clarify things for you.