Current density,

$\overline{){\mathbf{J}}{\mathbf{=}}\frac{\mathbf{I}}{\mathbf{A}}}$

Where **I** is the current and **A** is the area.

Area,

$\overline{){\mathbf{A}}{\mathbf{=}}{\mathbf{\pi}}{{\mathbf{\left(}}\frac{\mathbf{d}}{\mathbf{2}}{\mathbf{\right)}}}^{{\mathbf{2}}}}$

Where **d** is the diameter.

A)

Assume that I_{3} enters the junction.

d_{1} = 2.1 mm

d_{2} = 3.0 mm

J_{1} = 4.0 A/mm^{2}

J_{2} = 5.7 A/mm^{2}

The magnitudes of the current density and the diameters for wires 1 and 2 are given in the table. The current directions are indicated by the arrows.

Wire | Current density (A/mm ^{2}) | Diameter (mm) |

1 | 4.0 | 2.1 |

2 | 5.7 | 3.0 |

A) Find the Current I_{3} in wire 3. Express your answer in amperes to two significant figures. Call current out of the junction positive and current into the junction negative.

B) Find the magnitude of the current density J_{3} in wire 3. The diameter of wire 3 is 1.5mm. Express your answer in amperes per square millimeter to two significant figures.

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