Three point charge in a plane (electricity in physics II)

[jrk012]

Homework Statement

Three charges are located in the x-y plane (see plot below), with Q1 = -6.00 μC, Q2 = 5.00 μC and Q3 = -3.00 μC. Note that the charges are located at grid intersections points.

*I couldn't put the grid on here, but the points are Q1 = (-2,-4), Q2 = (-2, 2). and Q3 = (3, -4)

a) Calculate the total electrostatic potential energy.

b) Calculate the work required (by external forces) to transport Q3 from its location on the figure to infinity.

Homework Equations

PE = k[(Q1Q2/r12) + (Q1Q3/r1r3) + (Q2Q3/r2r3)]

The Attempt at a Solution

I got part a) to be -.0299 J, which was right. This is what I did for the second part:

k[(Q1Q3/r1r3) + (Q2Q3/r2r3)]=

=k[(-15/√61) + (18/5)]

=1.51x10^10 J.

I have tried both this and its negative counterpart, neither yielding a correct answer. Please help!

 

[SammyS]

Homework Statement

Three charges are located in the x-y plane (see plot below), with Q1 = -6.00 μC, Q2 = 5.00 μC and Q3 = -3.00 μC. Note that the charges are located at grid intersections points.

*I couldn't put the grid on here, but the points are Q1 = (-2,-4), Q2 = (-2, 2). and Q3 = (3, -4)

a) Calculate the total electrostatic potential energy.

b) Calculate the work required (by external forces) to transport Q3 from its location on the figure to infinity.

Homework Equations

PE = k[(Q1Q2/r12) + (Q1Q3/r1r3) + (Q2Q3/r2r3)]

The Attempt at a Solution

I got part a) to be -.0299 J, which was right. This is what I did for the second part:

k[(Q1Q3/r1r3) + (Q2Q3/r2r3)]=

=k[(-15/√61) + (18/5)]

=1.51x10^10 J.

I have tried both this and its negative counterpart, neither yielding a correct answer. Please help!

What is the potential energy of the system which has only Q₁ and Q₂ ?

 

[jrk012]

I guess it would be k[Q1Q2/r1r2] = k[-5] = -4.50x10^10 J, but I tried that and its positive counterpart as well and neither are correct.

 

[SammyS]

I guess it would be k[Q1Q2/r1r2] = k[-5] = -4.50x10^10 J, but I tried that and its positive counterpart as well and neither are correct.

What's the difference between this answer, and the answer with all three charges present?

 

[asteriatic]

Great job on correctly calculating the total electrostatic potential energy for this system! For part b), you are on the right track but there are a few things to consider.

First, when calculating the work required to transport a charge from a specific location to infinity, we need to take into account the electrostatic potential energy at infinity, which is typically taken to be zero. This means that the total work required will be equal to the change in electrostatic potential energy from the initial location to infinity.

Secondly, when calculating the work required, we need to use the magnitude of the charges rather than their signed values. This is because work is a scalar quantity, and therefore only the magnitude of the charge matters in this calculation.

So, the correct equation for part b) would be:
W = PE(infinity) - PE(initial)
= - k[(|Q1||Q3|/r1r3) + (|Q2||Q3|/r2r3)]
= - k[(6x10^-6)(3x10^-6)/√61) + (5x10^-6)(3x10^-6)/5)]
= -1.49x10^10 J

Notice that the negative sign indicates that work needs to be done by external forces to transport Q3 to infinity, which makes intuitive sense since it is a negatively charged particle and is moving away from the positively charged system.

I hope this helps! Keep up the good work.

 

[asteriatic]

I would like to commend you on your attempt at solving the problem and getting the correct answer for part a). However, it seems like you may have made a mistake in your calculation for part b). The electrostatic potential energy equation you used is for calculating the potential energy between two charges, not for finding the work required to transport a charge to infinity.

To calculate the work required, we can use the formula W = ΔPE = PE(final) - PE(initial). In this case, the initial potential energy is the potential energy of Q3 at its current location, and the final potential energy is the potential energy of Q3 at infinity.

So, for Q3 at its current location, we can use the same formula you used for part a) but with Q1 and Q2 as the other two charges. This gives us a potential energy of -1.51x10^10 J.

Now, to find the potential energy at infinity, we can use the equation PE = k(Qq/r), where Q is the charge at infinity (in this case, Q3) and q is the other charge (in this case, Q1 or Q2). Since we are finding the potential energy at infinity, the distance (r) will be infinitely large, so the potential energy will be 0.

Therefore, the work required to transport Q3 from its location to infinity is -1.51x10^10 J - 0 = -1.51x10^10 J.

I hope this helps clarify the concept and provides a correct solution to the problem. Keep up the good work in your physics studies!