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Setup 1

An object \$(\epsilon, \mu)\$ occupies volume \$V_1\$ and is enclosed by surface \$S_1\$. It sits in vacuum \$(\epsilon_0, \mu_0)\$, denoted by \$V_0\$. In \$V_0\$ there is an electric field \$\vec{E}_\mathrm{inc}\$ which impinges on said object. As a result, a set of fields \$(\vec{E}_1, \vec{H}_1)\$ is established inside \$V_1\$.

We know that we can introduce equivalent current sources on \$S_1\$, which generate the correct fields \$(\vec{E}_1, \vec{H}_1)\$ inside \$V_1\$, but exactly cancel ("extinct") the field outside, so that the total field in \$V_0 \backslash V_1\$ is \$0\$.

Setup 2

Now suppose that in addition to the first object, we introduce another object which occupies volume \$V_2\$ and is bounded by surface \$S_2\$, and has the same material properties as the first object \$(\epsilon, \mu)\$.

I know that the equivalence principle can be applied individually to each object one at a time, to study the fields generated inside them.

However, does anything prevent me from treating these objects as one, i.e. \$V_1 \cup V_2\$ and \$S_1 \cup S_2\$? In other words, can I simultaneously introduce equivalent currents which exist on \$S_1\$ and equivalent currents that exist on \$S_2\$, which collectively generate the correct fields inside both objects, and collectively generate a \$0\$ field in \$V_0 \backslash (V_1 \cup V_2)\$?

I couldn't find any clear references to such a situation online; any insight would be appreciated. Thanks!

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