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Electromagnetism. Electromagnetism Canadas Triumph Accelerator Putting it All Together Hydrogen Minus Initial Acceleration Electrostatic Circular Motion.

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Presentation on theme: "Electromagnetism. Electromagnetism Canadas Triumph Accelerator Putting it All Together Hydrogen Minus Initial Acceleration Electrostatic Circular Motion."— Presentation transcript:

1 Electromagnetism

2 Electromagnetism Canadas Triumph Accelerator Putting it All Together Hydrogen Minus Initial Acceleration Electrostatic Circular Motion Magnetic Steering Filtering

3 Electromagnetism Review Magnetic Flux We can describe the Density (or amount) of a Magnetic Field with the concept of Magnetic Flux. Flux can be described as the total number of lines passing though an area, loop or coil. It is a quantity of convenience used in Faradays Law.

4 Electromagnetism Review Flux can be described as the total number of lines passing though an area, loop or coil. Magnetic Flux Magnetic Field (Tesla) Magnetic Field (Tesla) Area of Surface (m 2 ) Area of Surface (m 2 ) Angle between field and normal line (B ) on the Surface Area This can be described by the equation Magnetic Flux

5 Electromagnetism Review Magnetic Flux Observations The Stronger the Magnetic Field (B), the greater the Flux ( ). The larger the Area (A), the greater the Flux ( ). If the Magnetic Field (B) is perpendicular to the area, then the Flux ( ) will be at a maximum.

6 Electromagnetism Review Magnetic Flux Units Since B = BAcos( θ) Since B = BAcos( θ) Flux has the units of B x A This is (Tesla)(Metre 2 ) This is (Tesla)(Metre 2 ) This is also called a Weber (Wb)

7 Electromagnetism Review Magnetic Flux Units When the field is perpendicular to the plane of the loop θ = 0 and Φ B = Φ B, max = BA When the field is perpendicular to the plane of the loop θ = 0 and Φ B = Φ B, max = BA When the field is parallel to the plane of the loop. θ = 90° and Φ B = 0 The flux can be negative, for example if θ = 180° When the field is parallel to the plane of the loop. θ = 90° and Φ B = 0 The flux can be negative, for example if θ = 180° When the field is at an angle θ to the field B, Φ B is less than max.

8 Electromagnetism Review Magnetic Flux by Larger Area You can increase the magnetic Flux by increasing the Surface Area

9 Electromagnetism Review Magnetic Flux by Strengthening the Field You can increase the magnetic Flux by Strengthening the Field.

10 Electromagnetism Review Magnetic Flux Practice Question You have a hula loop of radius 0.5m that is immersed in the Earths 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 Earths North pole. What is the flux through the hoop?

11 Electromagnetism Review Induction Faradays Law describes the relationship between Electric Current and Magnetism. Faradays Law An Electric Current can induce a Magnetic Field, and a Magnetic Field can induce a Electric Current. Just as Electricity needs to be moving to create a Magnetic field B, The Magnetic field B needs to be moving to create an Electric Current.

12 Electromagnetism Review Law of Induction Induced Voltage, V. A voltage is generated a Magnetic Force has been traditionally called an Electromotive Force or emf. Induced Voltage, V. A voltage is generated a Magnetic Force has been traditionally called an Electromotive Force or emf. Faradays Law Change in Magnetic Flux, Wb Change in time, s The number of coils of wire The greater the change in Magnetic Flux 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. The greater the change in Magnetic Flux 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.

13 Electromagnetism Review Faradays Law Practice Question You have a coil of wire with 30 loops, each of which has an area of 2.0 x m 2. The Magnetic Field B is perpendicular to the surface. At time t=0 s, the Field B is measured at 1.0 T. At time, t=.2 s, the Field B is measured at 1.1 T. What is the average emf inside the coils.

14 Electromagnetism Review B Direction Lenzs Law describes the direction of the Electric Current produced by a changing Magnetic Field. Lenzs Law The Thumb points in the direction of the Current. The fingers curl in the direction of the Magnetic Field.

15 Electromagnetism Review B Direction An influenced emf gives rise to a Electric Current whose Magnetic Field opposes the original change in Flux. Lenzs Law The Right Hand Rule can aid us in these situations.

16 Electromagnetism Review Lenzs Law X X X X X X X Notice how the area is lessened when the loop is stretched. Since the Flux is reduced, the Electric Current flows in the direction that would produce the B field. This direction tries to help maintain the original Flux. Change in Flux The induced current attempts to maintain the status quo.

17 Electromagnetism Review Lenzs Law Hoop Entering B Field X X X X X X X When the loop enters a Magnetic Field. An Electric Current is induced (counter clockwise) in the loop as to oppose the increase in the Flux inside the loop. X X X X X X X

18 Electromagnetism Review Lenzs Law Hoop Inside B Field X X X X X X X When the loop is total immersed inside a Magnetic Field there is No increase in Flux therefore there is No Current flow in the loop.

19 Electromagnetism Review Lenzs Law Hoop Exiting B Field X X X X X X X When the loop exits a Magnetic Field. An Electric Current is induced (clockwise) in the loop as to oppose the decrease in the Flux inside the loop. X X X X X X X

20 Electromagnetism Review Lenzs Law Magnet Moving Through Hoop When a magnet passes through a closed loop, the current will flow in what directions? When a magnet enters the loop the current will flow clockwise (to oppose the increase in flux, make the end of the loop the magnet enters 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). NS

21 When the North end of a magnet enters the loop from behind the screen, which direction, if any, will the current flow in the wire? Electromagnetism Review Lenzs Law Magnet Moving Through Hoop The current will flow clockwise to oppose the increasing flux.

22 Electromagnetism Review EMF induced in a Moving Conductor 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 Flux inside the loop increases. EMF

23 Electromagnetism Review EMF in a Moving Conductor Induced Electromotive Force or emf. Faradays Law Velocity in m/s. Length of moving conductor in m. Magnetic Field in T.

24 Electromagnetism Review EMF induced in a Moving Conductor 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. EMF X X X X X X X X X X X

25 Electromagnetism Review EMF induced in a Moving Conductor EMF X X X X X X X X X X X

26 + v Force on 1 moving charge: F = q v B sin( ) Out of the page (RHR) Force on many moving charges: F = (q/t)(vt)B sin( ) = I L B sin( ) Out of the page! v L = vt B I = q/t ++++ distance Electromagnetism Review Force of Magnetic Field on Current Recall

27 Torque on loop is = L F sin( ) = ILWB sin( ) Force on sections B-C and A-D: F = IBW (length x width = area) LW = A Torque is = I A B sin( ) W L a b c d B I X F F Torque on Current Loop in B field a b c d F F

28 x x x x x x x x Understanding: Torque on Current Loop What is the torque on the loop below? < IAB < IAB = IAB = IAB > IAB > IAB = 0

29 Torque tries to line up the normal with B! (when normal lines up with B, =0, so =0! ) Even if the loop is not rectangular, as long as it is flat: = I A B sin (area of loop) Magnitude: = I A B sin Direction: N # of loops a b c d B normal F F Torque on Current Loop between normal and B

30 B Compare the torque on loop 1 and 2 which have identical area, and current. I Understanding: Torque (1) B I (2) 1) 1 > 2 2) 1 = 2 3) 1 < 2 Area points out of page for both! = 90 degrees = I A B sin

31 Motional EMF F = q v B sin( ) + v Potential Difference F d/q EMF = q v B sin( ) L/q = v B L B L v Velocity Moving + charge feels force downwards: Moving + charge still feels force downwards: B F Angle between v and B

32 Understanding Which bar has the larger motional emf? Which bar has the larger motional emf? a b v v ε = v B L sin( ) is angle between v and B Case a: = 0, so ε = 0 Case b: = 90, so ε = v B L a is parallel, b is perpendicular

33 Motional EMF circuit Direction of Current Direction of Current Direction of force (F=ILB sin( )) on bar due to magnetic field I = /R Magnitude of current Clockwise (+ charges go down thru bar, up thru bulb) To left, slows down Moving bar acts like battery = vBL B -+-+ V What changes if B points into page? = vBL/R

34 Motional EMF circuit I = /R = vBL/R Still to left, slows down Moving bar acts like battery = vBL B + - V x x x x x x x x x x x x x x x x x Direction of Current Direction of Current Direction of force (F=ILB sin( )) on bar due to magnetic field Magnitude of current Counter-Clockwise (+ charges go up thru bar, down thru bulb)

35 Understanding Increase Increase Stay the Same Stay the Same Decrease Decrease Suppose the magnetic field is reversed so that it now points OUT of the page instead of IN as shown in the figure. To keep the bar moving at the same speed, the force supplied by the hand will have to: F=ILB sin( )) B and v still perpendicular ( =90), so F=ILB just like before! X X X X X X X X X X X FmFm o o o o o o FmFm

36 Understanding True True False False Suppose the magnetic field is reversed so that it now points OUT of the page instead of IN as shown in the figure. To keep the bar moving to the right, the hand will have to supply a force in the opposite direction. Current flows in the opposite direction, so force direction from the B field remains the same! X X X X X X X X X X X FmFm o o o o o o FmFm

37 Applications of Magnetic Force 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.

38 Examples of Induced Current Any change of current in primary induces a current in secondary.

39 Induced Current The current in the primary polarizes the material of the core. 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. 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. 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. 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.

40 Transformers A transformer is a device used to change the voltage in a circuit. AC currents must be used. 75,000 V in the power lines 120 V in your house p = primary s = secondary

41 Generator A coil of wire turns in a magnetic field. The flux in the coil is constantly changing, generating an emf in the coil.

42 Applets Wires: Flux area: Electric/Magnetic Balance: Flux: Induced Current: Moving Bar: Generator:


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