# Change in Electric Potential from the Surface of a Conducting Sphere to Infinity

• jhfrey89
In summary, A physics student at Virginia Tech is seeking help on a concept involving an insulating spherical shell with a charge of +150.0 \muC distributed on its outer surface. They are trying to determine what a voltmeter would read if connected between a point on the outer surface and infinity. The student was initially confused about how to approach the problem but eventually realized their mistake in using the wrong units. Another user explained the concept of electric potential and how it relates to the work needed to bring a test charge from infinity to the surface of the sphere. The student was able to understand and solve the problem correctly.
jhfrey89
Let me preface this as this is my first post on this forum. I'm a physics major at Virginia Tech and I've lurked the forum for a while to help understand concepts that may not be intuitive initially. I'm stuck on this one concept, so I decided to give posting a shot.

1. An insulating spherical shell with inner radius 25.0 cm and outer radius 60.0 cm carries a charge of + 150.0 $$\mu$$C uniformly distributed over its outer surface. Point a is at the center of the shell, point b is on the inner surface and point c is on the outer surface.

What will a voltmeter read if it is connected between c and infinity?

2. Given $$\int$$E*dl = V, I'd be integrating over infinity because it's an infinite path to... infinity.

3. It's more conceptual than anything, so I'm really at a loss. The change in potential from the center of the shell to the inner surface is 0V, and the change between the shell itself is 0V, as it's a conductor.

I'd rather just get the concept than someone spit out a solution.

Stupid me. I was right - I just messed up my units (read it as nano rather than micro).

Thanks anyways!

So then...how did you do this?

Well, think about it. If you have a charge, be it a point charge, sphere, or spherical shell, then it has some electric potential. If you bring in a test charge from infinity, you're going to have to do the that amount of work on it to bring it to the charge (assuming the point charge with the potential is a positive charge). It's the summation of all the work from infinity to the surface of the sphere.

My issue was that I was using a nanocoulomb rather than a microcoulomb, so I was off by a power of 10^3.

oh, I see. Makes sense. Thanks.

## 1. What is "Change in Electric Potential from the Surface of a Conducting Sphere to Infinity"?

The "Change in Electric Potential from the Surface of a Conducting Sphere to Infinity" refers to the difference in electric potential between the surface of a conducting sphere and an infinitely far point from the sphere.

## 2. How is the change in electric potential calculated for a conducting sphere?

The change in electric potential for a conducting sphere is calculated by taking the initial potential at the surface of the sphere and subtracting the potential at an infinitely far point. This can be expressed as V(infinity) - V(sphere).

## 3. What factors affect the change in electric potential for a conducting sphere?

The change in electric potential for a conducting sphere is affected by the charge on the sphere, the distance between the surface of the sphere and the infinitely far point, and the dielectric constant of the medium surrounding the sphere.

## 4. How does the change in electric potential relate to the electric field around a conducting sphere?

The change in electric potential is directly proportional to the electric field around a conducting sphere. This means that as the change in potential increases, the strength of the electric field also increases.

## 5. Why is the change in electric potential important to understand for conducting spheres?

The change in electric potential is important to understand for conducting spheres because it helps to determine the behavior and interactions of the sphere with other charged objects. It also plays a key role in understanding the distribution of charges on the surface of the sphere and the overall stability of the system.

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