## Ampère’s Law

8.5 Ampère’s Law

### Learning Objectives

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

- Explain how Ampère’s law relates the magnetic field produced by a current to the value of the current
- Calculate the magnetic field from a long straight wire, either thin or thick, by Ampère’s law

**Ampère’s law**

A fundamental property of a static magnetic field is that, unlike an electrostatic field, it is not conservative. A conservative vector field is one whose line integral between two end points is the same regardless of the path chosen. Magnetic fields do not have such a property. Instead, there is a relationship between the magnetic field and its source, electric current. It is expressed in terms of the line integral of and is known as **Ampère’s law**.

**Practice!**

Practice 8.5.1 |
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Evaluate the integral around a circular loop. |

A. 0 |

B. 2πR |

C. πR^{2} |

D. not enough information |

Practice 8.5.2 |
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Evaluate the integral around a square loop. |

A. 0 |

B. L^{2} |

C. 4L |

D. not enough information |

Practice 8.5.3 |
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Two identical Amperian loops are drawn in proximity to two identical current carrying wires. For which loop is the greatest? |

Practice 8.5.4 |
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Now compare loops B and C. For which loop is the greatest? |

Practice 8.5.5 |
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An Amperian loop is drawn around two current carrying wires. What is the value of , moving counterclockwise around the loop when viewed from above? |

A. µ_{0}I_{1} |

B. µ_{0}I_{2} |

C. µ_{0}(I_{1} + I_{2}) |

D. µ_{0}(I_{1} – I_{2}) |

E. 0 |

Practice 8.5.6 |
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An irregularly shaped Amperian loop is drawn around a wire carrying a current I. What is the value of , moving counterclockwise around the loop when viewed from above? |

A. µ_{0}I |

B. -µ_{0}I |

C. µ_{0}I sin |

D. µ_{0}I cos |

E. µ_{0}I tan |

F. 0 |