Electric potential and electric potential energy question

In summary, the question asks for the total electric potential energy of three charges placed at the corners of an equilateral triangle. The charges are +4.0^-6 c, +2.0^-6 c, and -4.0^-6 c, with sides of length 2.0 m. To solve, one must find the work needed to bring the charges into this configuration and calculate the voltage at the midpoint of each side using the V = kq/r equation.
  • #1
firebug
5
0
the question, from the Nelson Physics 12 texbook, is :

Three charges are placed at the corners of an equilateral triangle with sides of length 2.0 m. the charges, in clockwise starting at the top of the triangle are (c being coulombs) +4.0^-6 c, +2.0^-6 c, and -4.0^-6 c. a) calculate the total electric potential energy of the group of charges. b) determine the electric potential at the midpoint of each side of the triangle.

Just curious, if anyone could inform me of the steps of how to solve, that would be nice, i can take it from there. thanks in advance. :biggrin:

-firebug
 
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  • #2
The potential can be calculated by finding the work needed to bring the 3 charges into the said configuration (from infinity). Start with one charge, bring in the second, then the third.

To determine electric potential, you can once again use basic principles and find the work needed to bring a test charge to the designated place. The voltage is then this work divided by the test charge. You will find that the superposition of the V = kq/r equation will generally apply however.
 
  • #3



I would be happy to help you with this question. To calculate the total electric potential energy of the group of charges, we can use the formula:

U = k * (q1 * q2)/r

Where U is the electric potential energy, k is the Coulomb's constant (9 x 10^9 Nm^2/C^2), q1 and q2 are the charges, and r is the distance between the charges.

In this case, we have three charges, so we need to calculate the potential energy for each pair of charges and then add them together.

For the first pair of charges (+4.0^-6 c and +2.0^-6 c), the distance between them is 2.0 m (since they are at the corners of the equilateral triangle). Plugging in the values, we get:

U1 = (9 x 10^9 Nm^2/C^2) * ((4.0^-6 C) * (2.0^-6 C))/2.0 m

= 7.2 x 10^-3 J

Similarly, for the second pair of charges (+2.0^-6 c and -4.0^-6 c), the distance between them is also 2.0 m. Plugging in the values, we get:

U2 = (9 x 10^9 Nm^2/C^2) * ((2.0^-6 C) * (-4.0^-6 C))/2.0 m

= -7.2 x 10^-3 J

Finally, for the third pair of charges (+4.0^-6 c and -4.0^-6 c), the distance between them is √3 m (using Pythagorean theorem). Plugging in the values, we get:

U3 = (9 x 10^9 Nm^2/C^2) * ((4.0^-6 C) * (-4.0^-6 C))/√3 m

= -6.2 x 10^-3 J

Therefore, the total electric potential energy of the group of charges is:

U = U1 + U2 + U3

= 7.2 x 10^-3 J - 7.2 x 10^-3 J - 6.2 x 10^-3 J

= -
 

1. What is electric potential?

Electric potential is the amount of electric potential energy per unit charge at a specific point in an electric field. It is measured in volts (V).

2. How is electric potential different from electric potential energy?

Electric potential is a measure of the electric field at a specific point, while electric potential energy is the energy a charged particle has due to its position in an electric field.

3. What is the formula for electric potential?

The formula for electric potential is V = U/q, where V is electric potential, U is electric potential energy, and q is charge.

4. How does distance affect electric potential?

Electric potential is inversely proportional to distance, meaning that as distance increases, electric potential decreases. This is because the electric field weakens as distance increases, resulting in a lower electric potential.

5. Can electric potential be negative?

Yes, electric potential can be negative. This indicates that the electric field is directed in the opposite direction of the force on a positive charge. It is a relative value, so a negative electric potential does not necessarily mean a negative amount of energy.

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