Force between two oppositely charged conducting spheres

In summary, the force between two separated spheres with charge Q and -Q is the same as the force between two oppositely charged point charges, assuming the charge distribution on each sphere is radially symmetric. This approximation is accurate at large distances and is also applicable to conducting spheres. However, at very large distances, the charge distribution is no longer radially symmetric and the force must be calculated using the exact solution in Smythe's "Static and Dynamic Electricity" textbook. Additionally, for a more serious problem, the force would need to be calculated using the dipole correction terms, as hinted at by the term "conducting spheres."
  • #1
AxiomOfChoice
533
1
...if the spheres are separated by a large distance - one with charge Q, the other with charge -Q - isn't the force between them just the same as the force between two oppositely charged point charges, since the electric field produced by one of the spheres "looks like" the field of a point charge to the other sphere?
 
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  • #2
If the charge distribution on each sphere is radially symmetric, the force between is the same as for two point charges. If they are conducting spheres, this is approximately true at large distances.
 
  • #3
Hi Axiom
The charge distribution is radially symmetric only at very large distances. There is an exact solution in Smythe "Static and Dynamic Electricity", 3rd Edition, page 128-129.
Bob S
 
  • #4
"Large distances" would also make conductance of spheres insignificant.

If this was an exam problem in a serious Electrodynamics course, I'd give an answer as the force from point-like charges + the dipole correction terms. That seems to be what the "conducting spheres" is hinting at.
 
  • #5
K^2 said:
"Large distances" would also make conductance of spheres insignificant.

If this was an exam problem in a serious Electrodynamics course, I'd give an answer as the force from point-like charges + the dipole correction terms. That seems to be what the "conducting spheres" is hinting at.

I'm not sure that would be enough..

If it were a serious question, I would assume the problem was to evaluate the charge distribution of two charged spheres, each in the others field.
The only information you have is that the spheres are equipotential surfaces...
We're looking for a solution to Laplace's equation in three dimensions with the stated boundary condition.
Probably not difficult to anyone rather more clever than I. :biggrin:
 

Related to Force between two oppositely charged conducting spheres

1. What is the formula for calculating the force between two oppositely charged conducting spheres?

The formula for calculating the force between two oppositely charged conducting spheres is given by Coulomb's law, which states that the force (F) is equal to the product of the two charges (q1 and q2) divided by the square of the distance (r) between them, multiplied by a constant (k). Mathematically, it can be expressed as F = (k*q1*q2)/r^2.

2. How does the distance between the two spheres affect the force between them?

The force between two oppositely charged conducting spheres is inversely proportional to the square of the distance between them. This means that as the distance between the spheres increases, the force between them decreases and vice versa.

3. What is the unit of measurement for the force between two oppositely charged conducting spheres?

The unit of measurement for the force between two oppositely charged conducting spheres is Newton (N). It is a derived unit in the International System of Units (SI) and is equivalent to 1 kilogram meter per second squared (kg*m/s^2).

4. Can the force between two oppositely charged conducting spheres be attractive or repulsive?

The force between two oppositely charged conducting spheres can be both attractive and repulsive, depending on the charges of the spheres. If the charges are of opposite signs, the force will be attractive, and if they are of the same sign, the force will be repulsive.

5. How does the magnitude of the charges affect the force between two oppositely charged conducting spheres?

The magnitude of the charges has a direct impact on the force between two oppositely charged conducting spheres. As the magnitude of the charges increases, the force between the spheres also increases, and vice versa. This relationship is directly proportional.

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