In the case of two metal objects, we can set the potential of each object as $V_1, V_2$. Then the code for a numerical solution in 2D is

    Needs["NDSolve`FEM`"];
    (*Define Boundaries*)air = Rectangle[{-5, -5}, {5, 5}];
    object1 = Disk[];
    object2 = Rectangle[{2, 0}, {2.5, 2}]; reg12 = 
     RegionUnion[object1, object2];
    reg = RegionDifference[air, reg12];
    mesh = ToElementMesh[reg, 
      MeshRefinementFunction -> 
       Function[{vertices, area}, 
        area > 0.001 (0.1 + 10 Norm[Mean[vertices]])]]
    mesh["Wireframe"]
    eq = Laplacian[u[x, y], {x, y}]; V1 = 1; V2 = -2;
    bc = {DirichletCondition[u[x, y] == V1, x^2 + y^2 == 1], 
       DirichletCondition[
        u[x, y] == 
         V2, (x == 2 || x == 2.5 && 0 <= y <= 2) || (y == 0 || 
           y == 2 && 2 <= x <= 2.5)]};
    U = NDSolveValue[{eq == 0, bc}, u, {x, y} ∈ mesh];
    
    ef = -Grad[U[x, y], {x, y}];

Visualisation of solution 

    {DensityPlot[U[x, y], {x, y} ∈ reg, 
      ColorFunction -> "Rainbow", PlotLegends -> Automatic, 
      FrameLabel -> Automatic, PlotPoints -> 50, 
      PlotRange -> {{-4, 4}, {-4, 4}}], 
     StreamDensityPlot[Evaluate[ef], {x, y} ∈ reg, 
      ColorFunction -> "Rainbow", PlotLegends -> Automatic, 
      FrameLabel -> {x, y}, StreamStyle -> LightGray, 
      VectorPoints -> Fine, PlotRange -> {{-1, 3}, {-1, 3}}]}

[![Figure 1][1]][1]

Update 1. Next code is devoted to solve electrostatic problem for combination of dielectric and conducting objects (glass cylinder and metal strip). For dielectric we  put electric charge $q_1$, and for metal we put potential $V_2$. Code:

    Needs["NDSolve`FEM`"];
    par = {eps1 -> 3.5, eps2 -> 1.0}; air = 
     Rectangle[{-5, -5}, {5, 5}];
    object1 = Disk[]; q1 = 1; vol1 = 
     NIntegrate[1, {x, y} ∈ object1]; rho1 = q1/vol1;
    object2 = Rectangle[{2, 0}, {2.5, 2}]; 
    rho[x_, y_] := rho1 Boole[{x, y} ∈ object1];
    eps[x_, y_] := 
     eps2 + (eps1 - eps2) Boole[{x, y} ∈ object1]; reg = 
     RegionDifference[air, object2];
    mesh = ToElementMesh[reg, 
      MeshRefinementFunction -> 
       Function[{vertices, area}, 
        area > 0.001 (0.1 + 10 Norm[Mean[vertices]])]]
    mesh["Wireframe"]
     V2 = -2; eq = 
     Inactive[Div][
       eps[x, y] Inactive[Grad][u[x, y], {x, y}], {x, y}] == -2 Pi rho[x, 
        y]; bc = 
     DirichletCondition[u[x, y] == V2, {x, y} ∈ object2];
    U = NDSolveValue[{eq /. par, bc}, u, {x, y} ∈ mesh];
    
    ef = -Grad[U[x, y], {x, y}];
    
Visualisation 
 

    {DensityPlot[U[x, y], {x, y} ∈ mesh, 
      ColorFunction -> "Rainbow", PlotLegends -> Automatic, 
      FrameLabel -> Automatic, PlotPoints -> 50, 
      PlotRange -> {{-4, 4}, {-4, 4}}], 
     StreamDensityPlot[Evaluate[ef], {x, y} ∈ reg, 
      ColorFunction -> "Rainbow", PlotLegends -> Automatic, 
      FrameLabel -> {x, y}, StreamStyle -> LightGray, 
      VectorPoints -> Fine, PlotRange -> {{-1, 3}, {-1, 3}}], 
     StreamDensityPlot[Evaluate[ef], {x, y} ∈ reg, 
      ColorFunction -> Hue, FrameLabel -> {x, y}, StreamStyle -> Blue, 
      PlotRange -> {{-1.5, 1.5}, {-1.5, 1.5}}, PlotLegends -> Automatic]}
 [![Figure 2][2]][2]    
    


  [1]: https://i.sstatic.net/uY6Ey.png
  [2]: https://i.sstatic.net/Aavj7.png