Why Is Voltage Not Zero at Infinity in This Electrostatic Scenario?

In summary, a point charge of -8 µC is surrounded by two thick, conducting spherical shells with different radii. The potential at infinity is unspecified, but if given a value, the potential at r = 0.1 m can be found by integrating from .1 m to .9 m and then adding the given value.
  • #1
jehan60188
203
1

Homework Statement



A point charge q = -8 µC is surrounded by two thick, conducting spherical shells of inner and outer radii a1 = 0.2 m, a2 = 0.3 m, a3 = 0.8 m, and a4 = 0.9 m respectively. The inner shell is uncharged; the outer shell has a net charge Q = -8 µC. At this point in the problem, the potential at infinity is unspecified. Do not assume it is zero.


If now you are given V(inf) = 1 x 105 V, find the potential at r = 0.1 m.


Homework Equations



V = ∫E*dr

The Attempt at a Solution




voltage from .1 m to .9m = -359672 + -149863 = -509535
(known from previous steps)

I have no idea how to get the voltage from .9m to infinity!
 
Physics news on Phys.org
  • #2
hi jehan60188! :smile:

the voltage difference from .9m to infinity is the same as it would be if the voltage at infinity was 0 :wink:
 
  • #3
kk, since the voltage between point A (.9 m) and B (infinity) needs to be 10^5 higher than if it were supposed to be zero, I integrate from .9 to infinity, and then add 10^5
thanks!
 

FAQ: Why Is Voltage Not Zero at Infinity in This Electrostatic Scenario?

Why is voltage not zero at infinity?

The concept of voltage is defined as the measure of electrical potential difference between two points. At infinity, there is no other point to compare the potential difference with, so the voltage cannot be zero. Additionally, the concept of infinity implies an infinite distance, and according to the inverse square law, the potential decreases with distance, but never reaches zero.

2. How does the voltage change as distance increases towards infinity?

As the distance increases towards infinity, the voltage decreases. This is because voltage is directly proportional to the inverse of distance, according to the inverse square law. As the distance increases, the voltage decreases, but it never reaches zero.

3. Does the voltage at infinity affect the behavior of a circuit?

Yes, the voltage at infinity can affect the behavior of a circuit. This is because the voltage at infinity is used as a reference point for measuring the voltage at other points in the circuit. Any changes in the voltage at infinity can affect the voltage at other points, and thus impact the behavior of the circuit.

4. Is voltage at infinity always positive?

No, the voltage at infinity can be positive, negative, or zero, depending on the specific situation. For example, if a positive charge is placed at infinity, the voltage at infinity will be positive. However, if a negative charge is placed at infinity, the voltage at infinity will be negative. In some cases, the voltage at infinity can also be zero.

5. How does the voltage at infinity relate to electric potential energy?

The voltage at infinity is directly related to the electric potential energy. The voltage at a point is equal to the change in electric potential energy per unit charge at that point. Since the voltage at infinity is the reference point for measuring voltage, it is also the reference point for measuring electric potential energy. Therefore, the voltage at infinity plays a crucial role in determining the electric potential energy of a system.

Similar threads

Distances where electrostatic potential is zero
Replies
9
Views
3K
Electric Potential: Two Spherical Shells
Replies
1
Views
3K
What happens when one of two cocentric spherical shells is grounded?
Replies
11
Views
4K
How Does Charging a Conducting Shell Affect Potential Difference?
Replies
7
Views
2K
Potential energy in concentric shells
2
Replies
64
Views
9K
Electric Potential at Center of Sphere
Replies
8
Views
9K
Define the potential to be zero at infinity
Replies
7
Views
31K
Detecting the Alignment of an Inf. Plane Capacitor: A Paradox?
Replies
3
Views
1K
Work done in moving a charge to infinity
Replies
9
Views
7K
Electric Potential: Electric charge surrounded by two spherical shells
Replies
2
Views
4K

Hot Threads

Recent Insights

Back
Top