Chapter 29PowerPoint PresentationSlide 3Slide 4Slide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Chapter 29Magnetic Fields due to Currents29.2: Calculating the Magnetic Field due to a CurrentThe magnitude of the field dB produced at point P at distance r by a current length element i ds turns out to bewhere  is the angle between the directions of and , a unit vector that points from ds toward P. Symbol 0 is a constant, called the permeability constant, whose value isTherefore, in vector form29.2: Magnetic Field due to a Long Straight Wire:Fig. 29-3 Iron filings that have been sprinkled onto cardboard collect in concentric circles when current is sent through the central wire. The alignment, which is along magnetic field lines, is caused by the magneticfield produced by the current. (Courtesy EducationDevelopment Center)The magnitude of the magnetic field at a perpendicular distance R from a long (infinite) straight wire carrying a current i is given by29.2: Magnetic Field due to a Long Straight Wire:Fig. 29-4 A right-hand rule gives the direction of the magnetic field due to a current in a wire. (a) The magnetic field B at any point to the left of the wire is perpendicular to the dashed radial line and directed into the page, in the direction of the fingertips, as indicated by the x. (b) If the current is reversed, at any point to the left is still perpendicular to the dashed radial line but now is directed out of the page, as indicated by the dot.29.2: Magnetic Field due to a Long Straight Wire:29.2: Magnetic Field due to a Current in a Circular Arc of Wire:29.3: Force Between Two Parallel Wires:29.3: Force Between Two Parallel Wires, Rail Gun:29.4: Ampere’s Law:Curl your right hand around the Amperian loop, with the fingers pointing in the direction of integration. A current through the loop in the general direction of your outstretched thumb is assigned a plus sign, and a current generally in the opposite direction is assigned a minus sign.29.4: Ampere’s Law, Magnetic Field Outside a Long Straight Wire Carrying Current:29.4: Ampere’s Law, Magnetic Field Inside a Long Straight Wire Carrying Current:Example, Ampere’s Law to find the magnetic field inside a long cylinder of current.29.5: Solenoids and Toroids:Fig. 29-17 A vertical cross section through the central axis of a “stretched-out” solenoid. The back portions of five turns are shown, as are the magnetic field lines due to a current through the solenoid. Each turn produces circular magnetic field lines near itself. Near the solenoid’s axis, thefield lines combine into a net magnetic field that is directed along the axis. The closely spaced field lines there indicate a strong magnetic field. Outside the solenoid the field lines are widely spaced; the field there is very weak.29.5: Solenoids:Fig. 29-19 Application of Ampere’s law to a section of a long ideal solenoid carrying a current i. The Amperian loop is the rectangle abcda.Here n be the number of turns per unit length of the