Surface charge distribution of two metal spheres

In summary, the total charge Q is shared by two metal spheres of radii R1 and R2 connected by a long thin wire of length L. The charge on each sphere can be calculated using the equation Q1 = Q/(1+R2/R1), and the tension in the wire can be calculated using the equation Tension = Q1Q2/(4pi*epsilon_0*(L+R1+R2)^2).
  • #1
jdstokes
523
1

Homework Statement



A total charge Q is shared by two metal spheres of small radii R1 and R2, that are connected by a long thin wire of length L. Fin (a) the charge on each sphre and (b) the tension in the wire.

Source: Haliday 4th edn chapter 26 q. 91, p. 738

The Attempt at a Solution



I'm a bit confused by this. I assume that since the potential must be uniform for a conductor, that we can make the equation

[itex]\frac{rQ}{4\pi\epsilon_0 R_1} = \frac{(1-r)Q}{4\pi\epsilon_0 R_2}[/itex]

from which we obtain

[itex]Q_1 = \frac{Q}{1 + R_2/R_1}[/itex].

But I suppose this is only valid if the length of L is sufficiently large that we can ignore the interaction energy of the two spheres right?
 
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  • #2
Perhaps I am correct, and merely

[itex]\mathrm{Tension} = \frac{Q_1 Q_2}{4\pi \epsilon_0 (L + R_1 +R_2)^2}[/itex]?
 
  • #3
You're correct for both parts.

However, they probably want tension in terms of the given parameter Q, not in terms of Q1 and Q2.
 

1. What is surface charge distribution?

Surface charge distribution refers to the arrangement of positive and negative charges on the surface of an object. In the case of two metal spheres, the surface charge distribution is the distribution of charges on the surface of each sphere.

2. How is surface charge distribution of two metal spheres related to electrical potential?

The surface charge distribution of two metal spheres is directly related to the electrical potential between them. The distribution of charges on the surface of each sphere affects the strength and direction of the electric field between them, which in turn affects the electrical potential.

3. What factors affect the surface charge distribution of two metal spheres?

The surface charge distribution of two metal spheres is affected by several factors, including the size and shape of the spheres, the distance between them, and the material they are made of. Additionally, the presence of any external electric fields or charges can also impact the distribution.

4. How can the surface charge distribution of two metal spheres be calculated?

The surface charge distribution of two metal spheres can be calculated using Coulomb's law, which describes the relationship between electric charges, distance, and force. The charges on each sphere, the distance between them, and the material properties can all be used to determine the surface charge distribution.

5. Why is understanding the surface charge distribution of two metal spheres important?

Understanding the surface charge distribution of two metal spheres is important for various applications in physics and engineering. It can help predict the behavior of electric fields and charges, which is essential for designing electrical circuits and devices. Additionally, it is crucial for understanding the behavior of charged particles in various systems, such as in plasma physics or particle accelerators.

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