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Question #42904

Difficulty: 8/10 | 🟢 Free

The Question

Two extensive homogeneous solid conductors, Medium 1 and Medium 2, are joined at a planar interface. Medium 1 has electrical resistivity $\rho_1 = \rho$ (in $\Omega\cdot\text{m}$ ) and free electron number density $n_1 = n$ (in $\text{m}^{-3}$ ). Medium 2 has electrical resistivity $\rho_2 = 2\rho$ and free electron number density $n_2 = 3n$ . A steady electric current flows across the interface. In Medium 1, the uniform electric field lines make an angle $\theta_1 = 60^\circ$ with the normal to the interface. Find the ratio of the drift speed of free electrons in Medium 2 to that in Medium 1, $\frac{v_{d2}}{v_{d1}}$ .

Options

A.
$\frac{\sqrt{7}}{12}$
B.
$\frac{1}{6}$
C.
$\frac{1}{3}$
D.
$\frac{\sqrt{13}}{6}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Electric Field Line Geometry|Equation of Continuity|Integration

Why This Question Is Tricky

Common Mistakes

This question tests the boundary conditions for steady current flow and the microscopic model of drift velocity.

The primary trap is assuming that electric field lines do not refract (leading to $J_2/J_1 = \rho_1/\rho_2$ ) or that the current density magnitude is conserved ( $J_1 = J_2$ ) like an incompressible fluid in a uniform pipe.

Students often misapply the continuity equation by ignoring the vector nature of current density, failing to realize that only the normal component of $J$ is continuous, while the tangential component of $E$ is continuous.

This forces the current streamlines to bend, changing the overall magnitude of $J$ and consequently the drift velocity.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Electric Charges and Fields - Class 12
Concept	Electric Field Line Geometry
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free