Physics 2102 Gabriela Gonz lez L L Note If wire is not straight compute force on differential elements and integrate 1 Wire with current i Magnetic field out of page What is net force on wire By symmetry F2 will only have a vertical component Notice that the force is the same as that for a straight wire and this would be true no matter what the shape of L R R L the central segment Principle behind electric motors Torque on a current loop Rectangular coil a x b current i Net force on current loop 0 But Net torque is NOT zero For a coil with N turns N I A B sin where A is the area of coil 2 We just showed NiABsin N number of turns in coil A area of coil Define magnetic dipole moment Right hand rule curl fingers in direction of current thumb points along As in the case of electric dipoles magnetic dipoles tend to align with the magnetic field where potential energy is a minimum Q p Qa Q QE QE 3 Magnetic force on a moving electric charge F qvxB Magnetic Force on a wire F iLxB Magnetic Torque on a magnetic dipole x B potential energy U B A magnetic dipole with a dipole moment of magnitude 0 02 J T is released from rest in a uniform magnetic field of magnitude 50 mT The rotation of the dipole due to the magnetic force on it is unimpeded When the dipole rotates through the orientation where its dipole moment is aligned with the magnetic field its kinetic energy is 0 70 mJ a What is the initial angle between the dipole moment and the magnetic field b What is the angle when the dipole is next momentarily at rest 4 A wire of 62 0 cm length and 13 g mass is suspended by a pair of flexible leads in a magnetic field of 0 440 T What are the magnitude and direction of the current required to remove the tension in the supporting leads Electric fields are created microscopically by electric charges fields of elementary particles electrons protons macroscopically by adding the field of many elementary charges of the same sign Magnetic fields are created microscopically by magnetic moments of elementary particles electrons protons neutrons macroscopically by adding many microscopic magnetic moments magnetic materials or by electric charges that move electric currents 5 When we computed the electric field due to charges we used Coulomb s law If one had a large irregular object one broke it into infinitesimal pieces and computed Which we can write as Magnetic fields are produced by electrical currents If you wish to compute the magnetic field due to a current in a wire you use the law of Biot and Savart Jean Baptiste Biot 1774 1862 i Felix Savart 1791 1841 Quantitative rule for computing the magnetic field from any electric current Choose a differential element of wire of length dL and carrying a current i The field dB from this element 0 4 x10 7 T m A at a point located by the vector permeability constant r is given by the Biot Savart Law Compare with 6
View Full Document
Unlocking...