cay with distance from the charge: First, we will examine how magnetic fields are created, then we will calculate their magnitude and direction.Permanent magnetsSome materials can be said to be natural magnets. These magnets don't appear to have any moving charge, so how can they set up magnetic fields? The answer is found at the atomic scale:Electrons circling an atom set up small magnetic fields. In most materials, these fields are aligned in a fairly random manner, so that all of these small fields cancel each other. In a magnet, however, these fields line up to create a net magnetic dipole, so that the object sets up a magnetic field in the surrounding space.CurrentA current is a moving charge. Moving charges set up magnetic fields. Thus, a current seems the logical way to create a magnetic field. There are two basic setups which can be used for this purpose:Calculating Magnetic Field StrengthEquationsThe Biot-Savart Law: in order to find the magnetic field (denoted by the symbol B) produced by a given current distribution, we have to integrate the field at a given test point, P, due to individual current displacements, ids:The equation for the field integral turns out to be a rather complicated one, known as the Biot-Savart Law: Ampre's Law: in cetain situations, this integral can be simplified by symmetry. In these situatins, we can use a more fundamental law, known as Ampre's Law. This law allows the calculation of the field from the amount of current enclosed by an arbitrary closed loop:The equation for the magnetic field in such a case turns out to be:Long, straight wire One of the two most commonly used magnetic field equations is that for a long, straight wire. This equation can be determined from Ampre's Law through the following setup:The equation is then derived as follows:Solenoids A solenoid is a tightly wound coil of wire carrying a uniform current i : The field inside a solenoid is approximately as shown in the followi...
