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BHAGWAN MAHAVIR COLLEGE OF ENGINEERING AND TECHNOLOGY SUBJECT: ENGINEERING ELECTROMAGNETICS TOPIC NAME:THE STEADY MAGNETIC FIELD BRANCH: ELECTRONICS & COMMUNICATION(5th Semester) PRESENTED BY: REGMI JANKI L (130060111035) GUIDE: Mrs. HENAL PATEL HOD: Mr.RAHUL GONAWALA INTRODUCTION The magnetic field exists due to a permanent magnet , which is a natural magnet.But in electromagnetic engineering a link between electric and magnetic field is required to be studied.Such a link is absent with magnetic field due to a natural magnet. The study of steady magnetic field ,existing in a given space ,produced due to the flow of direct current through a conductor is called “magnetostatics”. MAGNETOSTATICS is the branch of electromagnetics dealing with the effects of electric charges in steady motion (i.e, steady current or DC). The fundamental law of magnetostatics is Ampere’s law of force. Ampere’s law of force is analogous to Coulomb’s law in electrostatics. Magnetostatics AMPERE’S LAW OF FORCE law of force is the “law of action” between current carrying circuits. Ampere’s law of force gives the magnetic force between two current carrying circuits in an otherwise empty universe. Ampere’s law of force involves complete circuits since current must flow in closed loops. Ampere’s MAGNETIC FLUX DENSITY Ampere’s force law describes an “action at a distance” analogous to Coulomb’s law. In Coulomb’s law, it was useful to introduce the concept of an electric field to describe the interaction between the charges. In Ampere’s law, we can define an appropriate field that may be regarded as the means by which currents exert force on each other. MAGNETIC FLUX DENSITY 0 I1d l1 aˆ R12 B12 2 4 C1 R12 the magnetic flux density at the location of dl2 due to the current I1 in C1 FORCE ON A MOVING CHARGE A moving point charge placed in a magnetic field experiences a force given by F m Qv B Q v Id l Qv B The force experienced by the point charge is in the direction into the paper. LORENTZ FORCE If a point charge is moving in a region where both electric and magnetic fields exist, then it experiences a total force given by F F e F m qE v B The Lorentz force equation is useful for determining the equation of motion for electrons in electromagnetic deflection systems such as CRTs. THE BIOT-SAVART LAW The Biot-Savart law gives us the B-field arising at a specified point P from a given current distribution. It is a fundamental law of magnetostatics. THE BIOT-SAVART LAW P R Id l r r 0 I d l R B(r ) 3 4 R C TYPES OF CURRENT DISTRIBUTIONS Line current density (current) - occurs for infinitesimally thin filamentary bodies (i.e., wires of negligible diameter). Surface current density (current per unit width) occurs when body is perfectly conducting. Volume current density (current per unit cross sectional area) - most general. AMPERE’S CIRCUITAL LAW IN INTEGRAL FORM Ampere’s Circuital Law in integral form states that “the circulation of the magnetic flux density in free space is proportional to the total current through the surface bounding the path over which the circulation is computed.” B d l I 0 encl C APPLICATIONS OF AMPERE’S LAW Ampere’s law in integral form is an integral equation for the unknown magnetic flux density resulting from a given current distribution. B dl I 0 encl C Closed form solution to Ampere’s law relies on our ability to construct a suitable family of Amperian paths. An Amperian path is a closed contour to which the magnetic flux density is tangential and over which equal to a constant value. FUNDAMENTAL POSTULATES MAGNETOSTATICS OF Ampere’s law in differential form B 0 J No isolated magnetic charges B is solenoidal B 0 APPLYING STOKES’S THEOREM TO AMPERE’S LAW B dl B d s C S 0 I encl 0 J d s S Because the above must hold for any surface S, we must have B 0 J Differential form of Ampere’s Law VECTOR MAGNETIC POTENTIAL Since the magnetic flux density is solenoidal, it can be written as the curl of a vector field called the vector magnetic potential. B 0 B A MAGNETIC DIPOLE MOMENT The magnetic dipole moment can be defined as 2 m aˆ z Ib Direction of the dipole moment is determined by the direction of current using the right-hand rule. Magnitude of the dipole moment is the product of the current and the area of the loop. MAGNETIC FLUX The magnetic flux crossing an open surface S is given by Bds Wb S Wb/m2 B S C MAGNETIC FLUX AND VECTOR MAGNETIC POTENTIAL The magnetic flux across an open surface may be evaluated in terms of the vector magnetic potential using Stokes’s theorem: B d s A d s S A dl C S THANK YOU