Question

If the potential difference across the ends of a copper wire of \(100\) cm length is \(2\) V and the conductivity of copper is \[ 5.95\times10^7\ \mathrm{Sm^{-1}}, \] then the current per unit area (in \(\mathrm{Am^{-2}}\)) of the conductor is

• A. \(1.19\times10^8\)
• B. \(2.975\times10^7\)
• C. \(2.38\times10^6\)
• D. \(1.487\times10^7\)

Hint:

Current density is related to conductivity by \[ \boxed{ J=\sigma E, } \] where \[ \boxed{ E=\frac{V}{L}. } \]

Answer 1

The Correct Option is A

Step 1: Find the electric field. The electric field inside the conductor is \[ E=\frac{V}{L}. \] Given, \[ V=2\text{ V}, \qquad L=100\text{ cm}=1\text{ m}. \] Hence, \[ E=\frac21=2\ \mathrm{Vm^{-1}}. \]

Step 2: Use the relation between current density and electric field. Current density is \[ J=\sigma E, \] where \[ \sigma=5.95\times10^7\ \mathrm{Sm^{-1}}. \] Therefore, \[ J = 5.95\times10^7\times2 = 1.19\times10^8\ \mathrm{Am^{-2}}. \]

Step 3: Write the answer. Hence, \[ \boxed{1.19\times10^8\ \mathrm{Am^{-2}}.} \] Thus, \[ \boxed{(A)} \] is the correct answer.