Which of the following represents Ohm’s law for a conducting material?

The correct answer is Option (2) → \( \vec J = \sigma\vec E \)

Ohm’s law in its microscopic form says that the current density at a point is proportional to the electric field there, with the conductivity \( \sigma \) as the constant of proportionality, \( \vec J = \sigma\vec E \). Here \( \sigma = 1/\rho \), where \( \rho \) is the resistivity.

Why the other options are incorrect

• Option (1) \( R=VI \) — Incorrect. Resistance is the ratio \( R = V/I \), not the product.

• Option (3) \( \vec j = \rho\vec E \) — Incorrect. The resistivity \( \rho \) and the conductivity \( \sigma \) are inverses; the correct forms are \( \vec j = \sigma\vec E \) or \( \vec E = \rho\vec j \).

• Option (4) \( I= RV \) — Incorrect. The current is \( I = V/R \), so it falls as the resistance rises.

NCERT (2026-27):
Ohm’s Law – “… The current density, (which we have defined as the current through unit area normal to the current) is also directed along E, and is also a vector j (≡ j E/E). Thus, the last equation can be written as,

    \( \displaystyle \mathbf{E} = \mathbf{j}\rho \qquad (3.12) \)

    \( \displaystyle \text{or,}\quad \mathbf{j} = \sigma\,\mathbf{E} \qquad (3.13) \)

where \( \sigma \equiv 1/\rho \) is called the conductivity. Ohm’s law is often stated in an equivalent form, Eq. (3.13) in addition to Eq.(3.3).”