Distance from potential difference

In summary, we discussed finding the distance at which the electric potential of a metal sphere with a net charge of 4.2x10^-8C decreases by 500V. The solution involved using the equation V = kq/r for a charged conducting sphere, where all the charge is located at the surface. This behavior is determined through a mathematical proof, similar to Newton's gravitational shell theorem. The final answer was 0.0371 m, expressed in cm to match the given sphere radius.
  • #1
Sho Kano
372
3

Homework Statement


A metal sphere of radius 15 cm has a net charge of 4.2x10^-8C. At what distance from the sphere's surface has the electric potential decreased by 500V?

Homework Equations


V = kQ/r

The Attempt at a Solution


[itex]\Delta V\quad =\quad \frac { kQ }{ r } \\ \\ r\quad =\quad \frac { kQ }{ \Delta V } \\ r\quad =\quad \frac { 9e9*4.2e-8 }{ 500 } \\ =\quad 0.756\quad m[/itex]

What is wrong?
 
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  • #2
You are looking for a potential difference, not a particular potential. Find the potential difference between a point located adjacent to the sphere (ro ≅ 15 cm) and one located at some larger radius r1. Once you know r1 you should be able to find the required distance.
 
  • #3
gneill said:
You are looking for a potential difference, not a particular potential. Find the potential difference between a point located adjacent to the sphere (ro ≅ 15 cm) and one located at some larger radius r1. Once you know r1 you should be able to find the required distance.
In a metal sphere the charge is distributed to the surface right?
Can I use V = kq/r for a sphere? It seems a bit weird to me, can you explain? Maybe I just don't understand the voltage equation..
 
  • #4
Sho Kano said:
In a metal sphere the charge is distributed to the surface right?
Can I use V = kq/r for a sphere? It seems a bit weird to me, can you explain? Maybe I just don't understand the voltage equation..
For a charged conducting sphere, all the charge will be located at its surface. For any spherically symmetric charge distribution the electric field external to the sphere behaves as though the total charge were a point charge located at the center of the sphere.

So yes, you can use V = kq/r for the sphere.
 
  • #5
gneill said:
For a charged conducting sphere, all the charge will be located at its surface. For any spherically symmetric charge distribution the electric field external to the sphere behaves as though the total charge were a point charge located at the center of the sphere.

So yes, you can use V = kq/r for the sphere.
If it's not too much trouble, why does it behave like a point charge? Is it through some kind of mathematical proof?
 
  • #6
Sho Kano said:
If it's not too much trouble, why does it behave like a point charge? Is it through some kind of mathematical proof?
Yes. It's the same method as for Newton's gravitational shell theorem.
 
  • #7
gneill said:
Yes. It's the same method as for Newton's gravitational shell theorem.
Sorry, for the late response. The answer that I'm getting is 0.0371 m?
 
  • #8
Looks good. You should probably express it in cm since the sphere radius was given in those units.
 
  • #9
gneill said:
Looks good. You should probably express it in cm since the sphere radius was given in those units.
Good advice, the tricky part was just one of the steps involved putting d+r in the voltage equation.
Thanks for the help!
 

1. What is distance from potential difference?

Distance from potential difference is the physical distance between two points in an electric field where there is a difference in electric potential. It is measured in meters (m).

2. How is distance from potential difference related to electric potential?

The distance from potential difference is directly related to electric potential. As the distance increases, the electric potential decreases. This relationship follows an inverse square law, meaning that the electric potential decreases as the distance squared increases.

3. Why is distance from potential difference important in understanding electric fields?

Distance from potential difference is important in understanding electric fields because it helps us understand how the strength of an electric field changes as we move away from a source of charge. It also allows us to calculate the amount of work needed to move a charge between two points in an electric field.

4. Can distance from potential difference be negative?

No, distance from potential difference cannot be negative. It is a physical distance and therefore must be a positive value. Negative values may be encountered in calculations, but this simply represents the direction of the electric field.

5. How is distance from potential difference measured?

Distance from potential difference can be measured using a variety of techniques, such as using a ruler or measuring tape for shorter distances, a laser rangefinder for longer distances, or specialized instruments such as a voltmeter or multimeter for more precise measurements in an electric field.

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