A long straight wire of circular cross section

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 A fundamental property of a static magnetic field is that, unlike an electrostatic field, it is not conservative. A conservative field is one that does the same amount of work on a particle moving between two different points 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 [latex]\stackrel.[/latex] If the radius of this particular circle is r, the projection is [latex]rd\theta ,[/latex] and [latex]\oint \stackreld\theta =2\pi[/latex] and [latex]\oint \stackrelI[/latex] where I is the total current passing through any open surface S whose perimeter is the path of integration. Only currents inside the path of integration need be considered. To determine whether a specific current I is positive or negative, curl the fingers of your right hand in the direction of the path of integration, as shown in I passes through S in the same direction as your extended thumb, I is positive; if I passes through S in the direction opposite to your extended thumb, it is negative. Problem-Solving Strategy: Ampère’s Law To calculate the magnetic field created fro...

https://phys.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fphys.libretexts.org%2FBookshelves%2FUniversity_Physics%2FBook%253A_University_Physics_(OpenStax)%2FBook%253A_University_Physics_II_-_Thermodynamics_Electricity_and_Magnetism_(OpenStax)%2F12%253A_Sources_of_Magnetic_Fields%2F12.06%253A_Amperes_Law \( \newcommand\) • • • • • • • • 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 A fundamental property of a static magnetic field is that, unlike an electrostatic field, it is not conservative. A conservative field is one that does the same amount of work on a particle moving between two different points 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 \(\vec = 0.\] The extension of this result to the general case is Ampère’s law. Ampere's Law Over an arbitrary closed path, \[\oint \vec\). If I passes through S in the same direction as your extended thumb, I is positive; if I passes through S in the direction opposite to your extended thumb, it is negative. Problem-Solving Strategy: Ampère’s Law To calculate the magnetic field created from current in wire(s), use the following ...