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LECTURE 27 MAGNETIC FIELDS Instructor: Kazumi Tolich Lecture 27 2 ! Reading chapter 22-6 and 22-7. ! Magnetic field due to current ! Ampere’s law ! Current loops and solenoid Magnetism from moving charges 3 ! ! A moving charge generates a magnetic field. The magnetism inside bar magnets are due to electrons moving within the atoms. ! ! ! The orbiting electrons act like a magnet. If these tiny magnets line up, they act like a big magnet. According to the dynamo theory, Earth’s magnetic effects are due to electrically charged material flowing (convection of molten iron) inside Earth. Magnetic field due to current 4 ! ! Electric current can create magnetic fields. These magnetic fields form circles around the current. Direction of the magnetic field 5 ! The direction of the magnetic field can be found by the right hand rule. ! Point your thumb in the direction of the current, and your fingers will curl in the direction of the B field. The B field produced by a current 6 a) b) There is no current, so no B field is produced. With current, B field pointing perpendicular to the wire is produced. B due to current in a long straight wire 7 ! The magnitude of magnetic field at a distance r away from a long straight wire carrying a current I is given by µ0 I B= 2π r where µ0 = 4π × 10-7 T"m/A is the permeability of free space. Example: 1 8 ! A long, straight wire carries a current of I = 7.2 A. How far from this wire is the magnetic field it produces equal to the Earth’s magnetic field, which is approximately B = 5.0 × 10-5 T? Superposition of B 9 If there are multiple sources of magnetic field, the magnetic field at a particular location is the superposition of magnetic field due to each source. ! Since magnetic field is a vector quantity, you need to add magnetic field vectorially. ! Clicker question: 1 10 Example: 2 11 ! Two long parallel wires carrying currents i1 and i2 in opposite directions. What is the resultant magnetic field at point P? Assume i1 = 15 A, i2 = 32 A, and d = 5.3 cm. Ampere’s law 12 ! Ampere’s law relates the current through a surface defined by a closed path to the magnetic field along the path: ∑ B ΔL = µ I ! ! This 0 enclosed holds provided that the current is constant. Amperian loop 13 Ampere's law holds for any closed path. ! The closed path used in Ampere's law is called the amperian loop. ! An amperian loop is an imaginary path that you construct. ! If any two amperian loops enclose the same current, ∑ B!ΔL is the same, regardless of their shapes. ! Calculating B fields using Ampere's law 14 Ampere's law is true for all situations, but not useful in finding B unless the current is highly symmetric. ! In choosing the amperian loop: ! ! The B field is either parallel (B! ΔL = BΔL ) or perpendicular ( B! ΔL = 0 ) to the sections of the loop. ! If the B field is parallel to a section of the loop, the magnitude of the B field is constant along that part of the loop. Ampere’s law & I in a long straight wire 15 ! We can use Ampere’s law to find the magnetic field around a long, straight wire: ∑ B ΔL = µ I ! 0 enclosed B ( 2π r ) = µ0 I B= µ0 I 2π r Clicker question: 2 16 Force between wires 17 ! The magnetic field generated by wire 1 at wire 2 is µ 0 I1 B= 2π d ! The force on wire 2 is F = I 2 LB ! Therefore the force per unit length on either wire is F12 µ0 I1 I 2 = L 2π d d Demo: 1 18 ! Pinch wires ! Parallel hanging wires are either attracted or repelled by one another, depending on the directions of current in the wires. # Opposite direction: repel # Same direction: attract d The magnetic field lines due to a circular current loop 19 ! ! The magnetic field of a current loop is similar to the magnetic field of a bar magnet. In the center of the loop of radius R, N turns, carrying a current I, the magnetic field is given by N µ0 I B= 2R Magnetic field due to solenoid 20 ! ! A solenoid is a helix of closely spaced turns. The magnetic field inside a long solenoid is parallel to its axis. Infinite solenoid 21 ! We can use Ampere’s law to find the field inside the infinite solenoid: ∑ B ΔL = ∑ B ΔL + ∑ B ΔL + ∑ B ΔL + ∑ B ΔL ! ! 1 ! 2 = BL + 0h + 0L + 0h = BL ∑ B ΔL = µ I ! 0 enclosed = µ0 nLI B = µ0 nI n is the number of turns per unit length. ! 3 ! 4 Demo: 2 22 ! Magnetic fields around conductors ! Visualizing magnetic field using iron filings Demo: 3 23 ! Electromagnet ! A small electromagnet powered by a 1.5V battery that can hold several kilograms. ! A huge coil carries up to 25A; very strong field will attract nails, etc. that are thrown near. Electric bells 24 When a current is applied, B field is created, which attracts the clapper to the electromagnet. ! This breaks the circuit, collapsing the B field of the electromagnet. ! Switch Electromagnet Clapper