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Ohm’s law when applied to electromagnetic phenomenon gives the following expression :

  • A.\(\overline{J} = \sigma\overline{E}\)
  • B.V = IR
  • C.\(\sigma = \overline{J}\overline{E}\)
  • D.\(\overline{E} = \overline{J}\sigma\)

Answer: A

The field form of Ohm's law is \(\overline{J} = \sigma\overline{E}\).

In electromagnetic theory, Ohm's law is written at each point of a conductor: the current density is proportional to the electric field, with the conductivity \(\sigma\) as the constant of proportionality. Integrating it over a uniform wire of length L and cross-section A gives the circuit form \(V = IR\), with \(R = L/\sigma A\).

V = IR is the circuit law, not the expression for electromagnetic fields the question asks for. \(\sigma = \overline{J}\overline{E}\) multiplies where it should divide, and \(\overline{E} = \overline{J}\sigma\) puts the conductivity where the resistivity \(1/\sigma\) belongs.

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