Plotting Potential of 2 Charges: Solving 4πε0φ

[FS98]

Homework Statement

Consider the system of two charges shown in Fig. 2.8. Let z be the coordinate along the line on which the two charges lie, with z = 0 at the location of the positive charge. Make a plot of the potential φ (or rather 4πε0φ, for simplicity) along this line, from z = −5 m to z = 15 m.

Homework Equations

The Attempt at a Solution

I’m not sure what this question is asking? Figure 2.8 didn’t seem to be anywhere in the book. Are they asking for potential energy, or the flux or something else? I’m not quite sure what this question is asking.

Edit: I found the figure, and I’m pretty sure they want a plot of the electric gradient.

 

[Nguyen Son]

Excuse me, where is the figure?

 

[Nguyen Son]

Ah, so you meant that you didn't see figure 2.8 in the book?

 

[FS98]

Ah, so you meant that you didn't see figure 2.8 in the book?

Yeah, I looked through the entire chapter. The last figure seems to be marked 2.52, so I’m not really sure what’s going on here.

 

[Nguyen Son]

Bigggg problem Cuz without figure, we don't know the distance between two charges and sign of the second charge (positive or negative), and we can't do anything

 

[FS98]

Bigggg problem Cuz without figure, we don't know the distance between two charges and sign of the second charge (positive or negative), and we can't do anything

Just looked through it again. Apparently there are two sets of labeled figures. The correct one was at the beginning of the chapter, 46 pages away from the problem.

 

[tnich]

Homework Statement

Consider the system of two charges shown in Fig. 2.8. Let z be the coordinate along the line on which the two charges lie, with z = 0 at the location of the positive charge. Make a plot of the potential φ (or rather 4πε0φ, for simplicity) along this line, from z = −5 m to z = 15 m.

The problem is asking for a plot of the electric potential, which is the potential energy of a unit positive charge (or equivalently, the electrostatic potential energy of a charge divided by the charge). So imagine a particle with a charge of +1 on the z-axis. What is its potential energy?

 

[FS98]

The problem is asking for a plot of the electric potential, which is the potential energy of a unit positive charge (or equivalently, the electrostatic potential energy of a charge divided by the charge). So imagine a particle with a charge of +1 on the z-axis. What is its potential energy?

Wouldn’t the potential energy approach infinity because there is already a positive charge on the z- axis?

 

[tnich]

Wouldn’t it the potential energy approach infinity because there is already a positive charge on the z- axis?

Sure, the potential energy would approach infinity in some places, but not everywhere. There is also a negative charge on the z-axis.

 

[FS98]

Sure, the potential energy would approach infinity in some places, but not everywhere. There is also a negative charge on the z-axis.

Oops, for some reason I thought you meant at point z = 0. On the entire axis would it be 2kQq/(|r|) -kQq/(|r-3|)?

 

[tnich]

Oops, for some reason I thought you meant at point z = 0. On the entire axis would it be 2kQq/(|r|) -kQq/(|r-3|)?

That would be the potential energy of a charge q at z=r if Q = 6C. So you are part way there.

 

[FS98]

That would be the potential energy of a charge q at z=r if Q = 6C. So you are part way there.

So would the function that I have to plot be φ(z) = 12k/(|z|) - 6k/(|z-3|)?

Edit: Or rather 12/(|z|) - 6/(|z-3|), because it looks like the question wants a factor of k to be taken out?

 

[tnich]

That looks right to me.