---
title: "A solid conducting cube of side length \\(L\\) consists of two bonded rectangular slabs of identical dimensions \\(L \\times L \\times (L/2)\\) with uniform resistivities \\(\\rho_1\\) and \\(\\rho_2 = 3\\rho_1\\).  In Scenario 1, a potential difference \\(V_0\\) is applied across the opposite faces perpendicular to the interface such that current flows parallel to the interface.  In Scenario 2, the same potential difference \\(V_0\\) is applied across the opposite outer faces parallel to the interface such that current flows perpendicular to the interface.  What is the ratio \\(\\dfrac{E_{1,1}}{E_{1,2}}\\) of the electric field magnitude in the slab of resistivity \\(\\rho_1\\) in Scenario 1 to that in Scenario 2?"
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url: "https://nerd-notes.com/ubq/124906/"
date_modified: "2026-09-28T14:11:54+00:00"
---

# A solid conducting cube of side length \(L\) consists of two bonded rectangular slabs of identical dimensions \(L \times L \times (L/2)\) with uniform resistivities \(\rho_1\) and \(\rho_2 = 3\rho_1\).

In Scenario 1, a potential difference \(V_0\) is applied across the opposite faces perpendicular to the interface such that current flows parallel to the interface.

In Scenario 2, the same potential difference \(V_0\) is applied across the opposite outer faces parallel to the interface such that current flows perpendicular to the interface.

What is the ratio \(\dfrac{E_{1,1}}{E_{1,2}}\) of the electric field magnitude in the slab of resistivity \(\rho_1\) in Scenario 1 to that in Scenario 2?

A solid conducting cube of side length \(L\) consists of two bonded rectangular slabs of identical dimensions \(L \times L \times (L/2)\) with uniform resistivities \(\rho_1\) and \(\rho_2 = 3\rho_1\).

In Scenario 1, a potential difference \(V_0\) is applied across the opposite faces perpendicular to the interface such that current flows parallel to the interface.

In Scenario 2, the same potential difference \(V_0\) is applied across the opposite outer faces parallel to the interface such that current flows perpendicular to the interface.

What is the ratio \(\dfrac{E_{1,1}}{E_{1,2}}\) of the electric field magnitude in the slab of resistivity \(\rho_1\) in Scenario 1 to that in Scenario 2?

![An oblique grayscale perspective drawing of a single cube with side length L. A horizontal line across the front and right visible faces marks a planar seam dividing the cube into an upper slab and a lower slab of equal thickness. The upper slab is filled with light gray stippling and labeled \(\rho_1\) in its center. The lower slab has a plain white fill and is labeled \(\rho_2\) in its center. A vertical double-headed arrow along the left edge is labeled L. A horizontal double-headed arrow along the front bottom edge is labeled L. A receding double-headed arrow along the bottom right edge is labeled L. Two curly braces along the left front vertical edge indicate that each slab has a vertical thickness of L/2. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604713-K4A3ZA.jpg)

- **A.** \(1\)
- **B.** \(2\)
- **C.** \(3\)
- **D.** \(4\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124906/*