Find the value of the potential at the following distances

In summary, the problem involves a metal sphere with a distributed charge of 2.00 nC and a radius of 20.0 cm. The potential at specific distances from the center of the sphere (48.0 cm, 20.0 cm, and 12.0 cm) is being requested, with the potential at infinity being 0. The equation used is V=(kQ)/r, and while the potential at infinity does approach infinity, it is not the correct answer. For the second question, the potential at a point enclosed within the sphere cannot be assumed to be 0 without further information.
  • #1
Clement
6
0

Homework Statement


A total electric charge of 2.00 nC is distributed uniformly over the surface of a metal sphere with a radius of 20.0 cm. If the potential is zero at a point at infinity, find the value of the potential at the following distances from the center of the sphere.
(a) 48.0 cm
(b) 20.0 cm
(c) 12.0 cm


Homework Equations


V=(kQ)/r


The Attempt at a Solution


I got part a no problem, having difficulty with b and c
for b, when r approaches infinity, shouldn't the potential approach infinity? but infinity was not the right answer.
for c, when r is enclosed in the sphere, isn't the potential always going to be 0?

thanks
 
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  • #2
Clement said:

Homework Equations


V=(kQ)/r

Hmmm... this is the potential due to a point charge isn't it...why do you think this is also true for the uniformly charged spherical surface?


for b, when r approaches infinity, shouldn't the potential approach infinity? but infinity was not the right answer.

[tex]\frac{1}{\infty}=0\neq\infty[/tex]

for c, when r is enclosed in the sphere, isn't the potential always going to be 0?

Why would you say this?...When in doubt, go back to the mathematical definition of electrostatic potential...
 
  • #3
got it, thanks!
 

FAQ: Find the value of the potential at the following distances

What is the potential at a distance of 0?

The potential at a distance of 0 would be the potential at the point where the charge is located. This is because the potential at a point is defined as the work done per unit charge in bringing a test charge from infinity to that point. As the distance is 0, the test charge would not have to be moved and hence the work done would be 0.

How do you find the potential at a given distance?

To find the potential at a given distance, you would need to know the charge of the object creating the potential and the distance from the object. Then, you can use the formula V = kQ/r, where V is the potential, k is the Coulomb's constant, Q is the charge, and r is the distance. Plug in the values and you will get the potential at that distance.

Can the potential be negative at a certain distance?

Yes, the potential can be negative at a certain distance. This would indicate that the work done in bringing a test charge from infinity to that point is negative, meaning that work is being done by the field on the test charge rather than the test charge doing work on the field.

How does the potential change as distance increases?

As distance increases, the potential decreases. This is because the formula for potential is inversely proportional to the distance (V = kQ/r). As the distance increases, the denominator increases, leading to a decrease in the overall potential.

Can the potential at a distance of infinity ever be zero?

Yes, the potential at a distance of infinity can be zero. This would occur when the charge creating the potential is 0. In this case, there would be no force acting on a test charge and hence no work would be done in bringing it from infinity to that point, resulting in a potential of 0.

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