# Calculating voltage from multiple point charges

• Eric_meyers
In summary, the electric potential at a point 8 km above the ground and on the vertical line passing through three point charges located at different heights was calculated using the equation kq1/r1 + kq2/r2. The charges were converted from km to m and the negative charge was subtracted from the positive charges. The resulting value was 7.5E7.
Eric_meyers

## Homework Statement

A point charge 10 km in the air with a charge of 40 coulombs
A point charge 5 km in the air with a charge of -40 coulombs
A point chare 2 km in the air with a charge of 10 coulombs
-Find the electric potential due to these charges at a point which at a height of 8 km and on the vertical line passing through the charges.

kq1/r1 + kq2/r2

## The Attempt at a Solution

So I summed them up

v = k (40C/2000m - 40C/3000m + 10C/6000m) = 7.5E7

My question is, is do I need to convert km to m and was I correct in subtracting the negative 40 coulomb charge from the rest of the positive charges?

Yes and yes. Looks good to me.

I would like to clarify a few things. First, it is important to note that the equations used in this problem are for calculating the electric potential, not voltage. Voltage is a measure of electric potential difference, while electric potential is a measure of the electric potential energy per unit charge at a given point in space.

Now, to answer your question, yes, it is important to convert all units to the same base unit for consistency. In this case, since the charges are given in coulombs and the distances are given in kilometers, it would be best to convert the distances to meters (1 km = 1000 m). This will ensure that all units are in SI units and will give you the correct answer.

As for your calculation, you were correct to subtract the negative 40 coulomb charge from the rest of the positive charges. This is because the negative charge will have an opposite effect on the electric potential compared to the positive charges. In other words, the electric potential due to the negative charge will be negative, while the electric potential due to the positive charges will be positive. By subtracting the negative charge, you are taking into account its opposite effect on the overall electric potential.

In summary, it is important to convert all units to the same base unit and your calculation was correct in subtracting the negative charge from the positive charges. However, it is important to clarify that the result of your calculation is the electric potential, not voltage.

## 1. How do I calculate the total voltage from multiple point charges?

To calculate the total voltage from multiple point charges, you will first need to find the individual voltages of each point charge using the formula V=kQ/r, where k is the Coulomb's constant, Q is the charge of the point charge, and r is the distance between the point charge and the point where you want to calculate the voltage. Then, add all of the individual voltages together to get the total voltage.

## 2. Can I use the superposition principle to calculate voltage from multiple point charges?

Yes, the superposition principle states that the total voltage at a point is equal to the sum of the individual voltages from each point charge. This means you can use the formula V=kQ/r for each point charge and then add the results together to get the total voltage.

## 3. How do I know which direction the voltage is pointing when calculating from multiple point charges?

The direction of the voltage is determined by the sign of the point charge. If the charge is positive, the voltage will point away from the charge, and if the charge is negative, the voltage will point towards the charge. You can also use the convention that positive voltages are shown as (+) and negative voltages as (-).

## 4. What is the unit of measurement for voltage?

The unit of measurement for voltage is the volt (V). This unit is equivalent to joules per coulomb (J/C), which represents the amount of energy per unit charge.

## 5. Can I calculate the voltage at any point in space from multiple point charges?

Yes, you can calculate the voltage at any point in space as long as you know the charge and distance of each point charge from that point. Keep in mind that the voltage will decrease as you move further away from the point charges.

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