Electromagnetism Canada s Triumph Accelerator Putting it All Together Hydrogen Minus Electromagnetism Initial Acceleration Electrostatic Circular Motion Magnetic Steering iltering Magnetic lux Magnetic lux lux can be described as the total number of lines passing though an area, loop or coil. We can describe the Density (or amount) of a Magnetic ield with the concept of Magnetic lux. lux can be described as the total number of lines passing though an area, loop or coil. It is a quantity of convenience used in araday s Law. Magnetic lux Acos Magnetic ield (Tesla) Angle between field and normal line () on the Surface Area Area of Surface (m 2 ) This can be described by the equation 1
Acos Magnetic lux Observations Magnetic lux Units The Stronger the Magnetic ield (), the greater the lux (). Since = Acos(θ) lux has the units of x A The larger the Area (A), the greater the lux (). This is also called a Weber (Wb) This is (Tesla)(Metre 2 ) If the Magnetic ield () is perpendicular to the area, then the lux () will be at a maximum. Magnetic lux Units Magnetic lux by Larger Area When the field is perpendicular to the plane of the loop θ = 0 and Φ = Φ, max = A When the field is parallel to the plane of the loop. θ = 90 and Φ = 0 The flux can be negative, for example if θ = 180 When the field is at an angle θ to the field, Φ is less than max. You can increase the magnetic lux by increasing the Surface Area 2
Magnetic lux by Strengthening the ield Magnetic lux Practice Question Acos You have a hula loop of radius 0.5m that is immersed in the Earth s magnetic field (5x10-5 T). The hula loop is oriented in such a way that the normal is tilted at an angle of 20 0 away from the Earth s North pole. What is the flux through the hoop? Acos r 2 cos You can increase the magnetic lux by Strengthening the ield..5 20 5 10 T 0 m cos 5 3.710 Wb 5 2 araday s Law araday s Law Induction Law of Induction araday s Law describes the relationship between Electric Current and Magnetism. An Electric Current can induce a Magnetic ield, and a Magnetic ield can induce a Electric Current. Induced Voltage, V. A voltage is generated a Magnetic orce has been traditionally called an Electromotive orce or emf. The number of coils of wire N t Change in Magnetic lux, Wb Change in time, s Just as Electricity needs to be moving to create a Magnetic field, The Magnetic field needs to be moving to create an Electric Current. The greater the change in Magnetic lux in a wire loop, the greater the Induced Current. Less time corresponds to a greater Induced Current. Adding more loops corresponds to a greater Induced Current. 3
N t araday s Law Practice Question Direction You have a coil of wire with 30 loops, each of which has an area of 2.0 x 10-3 m 2. The Magnetic ield is perpendicular to the surface. At time t=0 s, the ield is measured at 1.0 T. At time, t=.2 s, the ield is measured at 1.1 T. What is the average emf inside the coils. describes the direction of the Electric Current produced by a changing Magnetic ield. N t Acos N t 0.03V Acos 1.1 1.0 2.0 10 3 2 T T m cos 0 30 0.2s 0.0s The Thumb points in the direction of the Current. The fingers curl in the direction of the Magnetic ield. Direction Change in lux An influenced emf gives rise to a Electric Current whose Magnetic ield opposes the original change in lux. The Right Hand Rule can aid us in these situations. Notice how the area is lessened when the loop is stretched. Since the lux is reduced, the Electric Current flows in the direction that would produce the field. This direction tries to help maintain the original lux. The induced current attempts to maintain the status quo. 4
N S 03/12/2010 Hoop Entering ield Hoop Inside ield When the loop enters a Magnetic ield. An Electric Current is induced (counter clockwise) in the loop as to oppose the increase in the lux inside the loop. When the loop is total immersed inside a Magnetic ield there is No increase in lux therefore there is No Current flow in the loop. Hoop Exiting ield Magnet Moving Through Hoop When the loop exits a Magnetic ield. An Electric Current is induced (clockwise) in the loop as to oppose the decrease in the lux inside the loop. When a magnet enters the loop passes the through current will flow clockwise a closed loop, (to oppose the increase the current in flux, will make the end flow of in the what loop the magnet enters directions? act like a North Pole) then zero. As the magnet exits, the current will then flow counter clockwise (to oppose the decrease in flux, ie look like a South Pole). 5
EM Magnet Moving Through Hoop EM induced in a Moving Conductor When the North end of a The magnet current enters will the flow loop clockwise from to behind oppose the the screen, increasing which flux. direction, if any, will the current flow in the wire? We have a conducting bar moving across a U shaped wire. The magnetic field is coming out of the screen. As the bar moves across the wire, the amount of lux inside the loop increases. araday s Law EM EM in a Moving Conductor EM induced in a Moving Conductor Induced Electromotive orce or emf. Velocity in m/s. A 2.0 m rod is moving at 7 m/s perpendicular to a 1.2 T magnetic field heading into the screen. Determine the induced emf. Lv Magnetic ield in T. Length of moving conductor in m. X X X X X X X X X X X X X X X X X X X X 6
EM Recall EM induced in a Moving Conductor orce of Magnetic ield on Current Lv m 1.2T 2.0m7 s 17V X X X X X X X X X X X X X X X X X X X X orce on 1 moving charge: = q v sin() Out of the page (RHR) orce on many moving charges: = (q/t)(vt) sin() = I L sin() Out of the page! v v L = vt I = q/t distance Torque on Current Loop in field W d a L orce on sections -C and A-D: = IW Torque on loop is t = L sin(f) = ILW sin(f) Torque is I (length x width = area) c X b t = I A sin(f) LW = A d f a b c Understanding: Torque on Current Loop What is the torque on the loop below? 1 2 3 t < IA t = IA t > IA t = 0 7
Torque on Current Loop Understanding: Torque Magnitude: t = I A sinf f Direction: Torque tries to line up the normal with! (when normal lines up with, f=0, so t=0! ) Even if the loop is not rectangular, as long as it is flat: # of loops between normal and t = N I A sinf. (area of loop) I (1) Compare the torque on loop 1 and 2 which have identical area, and current. Area points out of page for both! 1) t 1 > t 2 2) t 1 = t 2 3) t 1 < t 2 t = I A sinf (2) f = 90 degrees - v L - Motional EM Moving charge feels force downwards: v = q v sin() Velocity Moving charge still feels force downwards: Potential Difference d/q EM = q v sin() L/q = v L Angle between v and Understanding Which bar has the larger motional emf? a b ε = v L sin() is angle between v and Case a: = 0, so ε = 0 Case b: = 90, so ε = v L v a is parallel, b is perpendicular v Velocity 8
Motional EM circuit Moving bar acts like battery = vl Magnitude of current I = /R = vl/r Direction of Current Clockwise ( charges go down thru bar, up thru bulb) Direction of force (=IL sin()) on bar due to magnetic field What changes if points into page? To left, slows down - V Motional EM circuit Moving bar acts like battery = vl Magnitude of current I = /R = vl/r Direction of Current Still to left, slows down x x V x - x x Counter-Clockwise ( charges go up thru bar, down thru bulb) Direction of force (=IL sin()) on bar due to magnetic field Understanding Suppose the magnetic field is reversed so that it now points OUT of the page instead of IN as shown in the figure. X o X o o X o X o X o v X o X o X o X o o X o X X o X o o X o X o X o X o X o X o X o o X o X m To keep the bar moving at the same speed, the force supplied by the hand will have to: Increase Stay the Same =IL sin()) Decrease and v still perpendicular (=90), so =IL just like before! Understanding Suppose the magnetic field is reversed so that it now points OUT of the page instead of IN as shown in the figure. X o X o o X o X o X o v X o X o X o X o o X o X X o X o o X o X o X o X o X o X o X o o X o X m To keep the bar moving to the right, the hand will have to supply a force in the opposite direction. True Lv Lv alse I R Current flows in the opposite direction, so force direction from the field remains the same! 9
Applications of Magnetic orce Examples of Induced Current Any change of current in primary induces a current in secondary. Electric currents (in a wire, in a plasma, in a fluid solution, inside an atom) produce a disturbance in the surrounding space called the magnetic field. This magnetic field produces forces on any other macroscopic or microscopic currents. Example: MRI: Magnetic field (several Tesla) from superconducting solenoid induces a net alignment of the microscopic currents inside each and every proton at the center of the Hydrogen atoms in your body. Induced Current Transformers A transformer is a device used to change the voltage in a circuit. AC currents must be used. The current in the primary polarizes the material of the core. The magnetic field of the primary solenoid is enhanced by the magnetic field produced by these atomic currents. This magnetic field remains confined in the iron core, and only fans out and loops back at the end of the core. Any change in the current in the primary (opening or closing switch) produces a change in the magnetic flux through the secondary coil. This induces a current in the secondary. 75,000 V in the power lines I Vp N s p I p Vs Ns p = primary s = secondary 120 V in your house 10
Generator A coil of wire turns in a magnetic field. The flux in the coil is constantly changing, generating an emf in the coil. Wires: lux area: Electric/Magnetic alance: Applets lux: Induced Current: Moving ar: Generator: 11