Four wires are soldered together at a small junction

PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Electric current and circuits · Electric current and circuits

Electricity, Magnetism and Electromagnetism, Ch Current, current density, conductivity and Ohm's law

Problem

Four wires are soldered together at a small junction. All currents are steady, so no charge piles up anywhere at the junction. Measurements give: 2.5 A2.5\,\mathrm{A} flowing into the junction along wire 1, 1.8 A1.8\,\mathrm{A} flowing into the junction along wire 2, and 3.1 A3.1\,\mathrm{A} flowing out of the junction along wire 3. ((a)) Using a closed surface that encloses the junction and cuts each of the four wires once, state the value of the outward flux ∮SJ⋅dA\oint_S \mathbf{J}\cdot d\mathbf{A} for this steady state. ((b)) Find the magnitude of the current in wire 4 and say whether it flows into or out of the junction.

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