## Model of Conduction in Metals

5.2 Model of Conduction in Metals

### Learning Objectives

By the end of this section, you will be able to:

- Define the drift velocity of charges moving through a metal
- Define the vector current density
- Describe the operation of an incandescent lamp

### Current Density

**Practice!**

Practice 5.2.1 |
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A copper cylinder is machined to have the following shape. The ends are connected to a battery so that a current flows through the copper. Which region has the greatest current density ? |

Practice 5.2.2 |
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A copper cylinder is machined to have the following shape. The ends are connected to a battery so that a current flows through the copper. Which region has the greatest magnitude of current, I? |

Practice 5.2.3 |
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A copper cylinder is machined to have the following shape. The ends are connected to a battery so that a current flows through the copper. Which region has the greatest conductivity ? |

Practice 5.2.4 |
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A copper cylinder is machined to have the following shape. The ends are connected to a battery so that a current flows through the copper. Which region has the greatest magnitude electric field ? |

Practice 5.2.5 |
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So far, we have concluded J is greatest in region B. (Using , and ) The ratio of diameters is A:B:C = 3:1:5. How much larger magnitude is the drift velocity v _{d} in region B compared to C? |

**Discuss!**

An 18-gauge copper wire (the size usually used for lamp cords), with a diameter of 1.02 mm, carries a constant current of 1.67 A to a 200-W lamp. The free-electron density in the wire is 8.5 x 10^{28} electrons per cubic meter. Suppose we replaced the wire with 12-gauge copper wire, which has twice the diameter of 18-gauge wire. If the current remains the same, what effect would this have on the magnitude of the drift velocity v_{d}?