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**Magnetic Fields Due To Currents**

Law of Biot and Savart Magnetic Field due to a Long Straight Wire Magnetic Field due to a Circular Arc of Wire Force Between Two Parallel Currents Ampere’s Law Magnetic Field Inside a Long Straight Wire Solenoids and Toroids Current Carrying Coil as a Dipole pps by C Gliniewicz

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A current passing through a wire creates a magnetic field around the wire. This is known because electromagnets are made by encircling an iron object with coils of wires. One can imagine some small length of wire, ds, with a current moving through the wire creating a magnetic field at some point a distance. R, from the wire at an angle, θ. We can determine the magnetic field element, d. The quantity, ₀, is called the permeability constant. The value of the permeability constant is an exact value. The vector form of the equation for the magnetic field element is called the Law of Biot and Savart. The magnetic field due to a long straight wire forms a circle around the wire. The magnetic field decreases with the radius. pps by C Gliniewicz

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If one grasps a long wire by with the right hand in such a way that the thumb points in the direction of the positive current flow, then one’s fingers will naturally curl around the wire, pointing in the direction of the magnetic field. Recall that the magnetic field points from north to the south pole. When two parallel wires have current moving through them, one can find the magnetic field due to one wire at the second wire. Then one can find the force on the wire due to the current and magnetic field. One can use the right hand rule to determine the direction of the force by pointing one’s fingers in the direction of the current and curling them to the direction of the magnetic field. The thumb then points in the direction of the force. Wires carrying parallel currents attract one another. Antiparallel currents repel each other. A rail gun uses this fact to cause a projectile to move at extremely high speeds. There is a method to determine the magnetic field from the current if symmetry exists with the object in question. pps by C Gliniewicz

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**Ampere’s Law describes how to calculate the magnetic field**

Ampere’s Law describes how to calculate the magnetic field. Although attributed to Ampere, this law was actually determined by Maxwell. The circle on the integral sign means that the scalar product is to be integrated around a closed loop. If one curls their fingers around the loop in the direction of integration, then the outstretched thumb points in the direction of the positive current. If a wire with a radius, R, has a current flowing through it, there is a magnetic field inside the wire, but it is only due to the current flowing inside the point in question at some distance, r, from the center. A solenoid is a coil of wire whose length is much greater than its diameter. The number of coils per unit length, n, is used to calculate the magnetic field at the center of the solenoid. pps by C Gliniewicz

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**A toroid is a solenoid which is curled into a donut shape**

A toroid is a solenoid which is curled into a donut shape. It creates a magnetic field at the center of the coils. The value, N, is the total number of turns in the toroid. In this equation, the radius is part of the term. That means that the magnetic field inside the wire varies with the radius, unlike the equation of the solenoid which has a constant magnetic field. A coil of wire with a current creates a magnetic field and thus can act like a magnetic dipole. The magnetic field, pointing along the axis of the loop, has a value pps by C Gliniewicz

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