Refer to the figure shown. An \(E\)-\(V\) battery and infinitely many solenoids of \(1!\), \(2!\), \(3!\) and so on. The number of loops is connected in parallel. Another circuit has each of the infinite number of corresponding identical solenoids having \(N\) loops and internal resistance \(R\) connected in parallel. This circuit is placed near but not in contact with the former circuit.

In terms of the variables given, determine the total current induced when the switch is closed.

**Details and Assumptions**:

\(V\) is read as Volts, the unit of potential difference.

All elements are Ohmic.

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