Question

A current of 2 A passes through a cylindrical rod with uniform cross-sectional area of 4 m$^2$ and resistivity of 100 $\Omega$-m. The magnitude of the electric field (E) measured along the length of the rod in V/m is _________ (in integer).

Hint:

Use the generalized Ohm's law: \(E = \rho J\). Always compute current density first (\(J = I/A\)) before applying resistivity.

Answer 1

Step 1: Relation between electric field and current density.
Ohm's law in terms of resistivity: \[ E = \rho \, J \] where \(E\) = electric field (V/m), \(\rho\) = resistivity (\(\Omega \, m\)), and \(J\) = current density (A/m\(^2\)). Step 2: Calculate current density.
\[ J = \frac{I}{A} \] Given current \(I = 2 \, A\), area \(A = 4 \, m^2\): \[ J = \frac{2}{4} = 0.5 \, A/m^2 \] Step 3: Calculate electric field.
\[ E = \rho J = 100 \times 0.5 = 50 \, V/m \] Final Answer: \[ \boxed{50} \]