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AP Physics C: E&M
11.3 Resistance, Resistivity, and Ohm’s Law
11.1 Electric Current
AdvancedMCQMathematicalProportional Analysis13k
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.
Composite conducting cube consisting of two layers with resistivities \(\rho_1\) and \(\rho_2\).
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?

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