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Unformatted text preview: Lab 5: The Biot-Savart law - magnetic fields due to current carrying coils 1 Introduction Coulombs law describes the electric field of a point charge q . It predicts that the magnitude of the elec- tric field- E at a point located at a distance r from the charge is proportional to the charge, and inversely pro- portional to r 2 . The direction of the electric field is along the radial direction from the point charge, and can be found by considering the force acting on (a unit positive) test charge. In an analogous manner, the Biot-Savart law describes the magnetic field due to a point charge moving with a velocity- v . Since a moving charge represents a current, this law can also be used to specify the magnetic field of a current car- rying element of infinitesimal length d- l . It is most commonly written in this form and is widely used to calculate the magnetic field generated by a system of current carrying coils. The purpose of this experiment is to verify the pre- dictions of the Biot-Savart law by measuring the mag- netic field produced by some simple configurations of coils. You will measure the magnetic fields associated with the following configurations. 1. One of the simplest derivations of the Biot-Savart law is a calculation using the field along the axis of symmetry of a current carrying loop of wire. This derivation can also give you the field at the center of the coil. You can measure the field as a function of current and test the derivation. This is useful because using a single coil is often the easiest method of producing a magnetic field. 2. The magnetic field produced by a single current carrying coil is not uniform - it varies as a func- tion of position. Consider a pair of identical coils (radius R ) that are separated by a distance equal to R . If the current flowing through each coil is in the same direction, then the magnetic field along the axis of symmetry is uniform at the point mid- way between the coils. This is one of the most convenient methods of producing a uniform mag- netic field at a desired spatial location. This con- figuration is known as a pair of Helmholtz coils (The magnetic field inside a long solenoid is also uniform. Such a field is often more difficult to implement because of spatial constraints). 3. If the currents in the two coils (separated by R ) are in opposite directions, the arrangement may be referred to as a pair of anti-Helmholtz coils . The field along the axis of symmetry is zero at the point midway between the coils. The mag- netic field varies linearly as a function of position in the vicinity of the midpoint. This spatial vari- ation of the field is called a field gradient, and using anti-Helmholtz coils is the most convenient method of generating field gradients. Such field gradients are widely used in magnetic resonance imaging, which is a powerful, noninvasive tech- nique used for obtaining highly resolved spatial images. When a sample (such as the human body) is placed in a field gradient, the precession fre-...
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