The problem involves two spherical conductors

$A_1$

and

$A_2$

connected by a copper wire. Let’s analyze and compute the equivalent capacitance of the system.

Given:

• 
  $A_1$ 

  and $A_2$ 

  are concentric spherical conductors.

• Radii of the spheres:
  $r_1$ 

  (inner) and $r_2$ 

  (outer).

• The medium is air, so the permittivity is
  $\varepsilon_0$ 

  .

Key Concepts:

1. Potential Difference Between the Spheres: The two conductors are connected by a wire, meaning they are at the same potential. As a result, the electric field exists only between the two spheres.
2. Capacitance of a Single Isolated Sphere: If only
   $A_2$ 

   existed as a spherical conductor, its capacitance would be: 

   $$C_{\text{single}} = 4 \pi \varepsilon_0 r_2.$$ 

3. Why the System is Equivalent to an Isolated Sphere: Since
   $A_1$ 

   is connected to $A_2$ 

   via a conducting wire, any charge added to $A_1$ 

   immediately flows to $A_2$ 

   , making the system behave as if there is only one conductor of radius $r_2$ 

   .

Equivalent Capacitance:

Thus, the capacitance of the system is:

$$C_{\text{equivalent}} = 4 \pi \varepsilon_0 r_2.$$

Final Answer:

The equivalent capacitance of the system is:

$$\boxed{4 \pi \varepsilon_0 r_2}.$$