Electromagnetism

Electromagnetism Canada’s Triumph Accelerator Putting it All Together Hydrogen Minus Initial Acceleration Electrostatic Circular Motion Magnetic Steering Filtering

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 Faraday’s Law.

Electromagnetism Review Magnetic Flux Flux can be described as the total number of lines passing though an area, loop or coil. Angle between field and normal line (B) on the Surface Area Magnetic Flux Magnetic Field (Tesla) Area of Surface (m2) This can be described by the equation

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.

Electromagnetism Review Magnetic Flux Units Since B = BAcos(θ) Flux has the units of B x A This is also called a Weber (Wb) This is (Tesla)(Metre2)

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

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

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

Electromagnetism Review Magnetic Flux Practice Question 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 200 away from the Earth’s North pole. What is the flux through the hoop?

Electromagnetism Review Faraday’s Law Induction Faraday’s Law describes the relationship between Electric Current and Magnetism. 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 .

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

Electromagnetism Review Faraday’s Law Practice Question You have a coil of wire with 30 loops, each of which has an area of 2.0 x 10-3 m2. 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.

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

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

Electromagnetism Review Lenz’s Law Change in Flux X X X X X X X 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. The induced current attempts to maintain the status quo.

Electromagnetism Review Lenz’s Law Hoop Entering B Field X X X X X X X 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.

Electromagnetism Review Lenz’s 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.

Electromagnetism Review Lenz’s Law Hoop Exiting B Field X X X X X X X 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.

Electromagnetism Review Lenz’s Law Magnet Moving Through Hoop 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). When a magnet passes through a closed loop, the current will flow in what directions? N S

Electromagnetism Review Lenz’s Law Magnet Moving Through Hoop The current will flow clockwise to oppose the increasing flux. 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 EMF 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.

Electromagnetism Review Faraday’s Law EMF in a Moving Conductor Velocity in m/s. Induced Electromotive Force or emf. Length of moving conductor in m. Magnetic Field in T.

Electromagnetism Review EMF 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. X X X X X X X X X X X

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

Force on 1 moving charge: Electromagnetism Review Recall Force of Magnetic Field on Current Force on 1 moving charge: F = q v B sin(q) Out of the page (RHR) q v + Force on many moving charges: F = (q/t)(vt)B sin(q) = I L B sin(q) Out of the page! v L = vt B I = q/t + Use large right hand. Then do demo 184. distance

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

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

Torque on Current Loop N t = I A B sinf Direction: normal Magnitude: f between normal and B Direction: Torque tries to line up the normal with B! (when normal lines up with B, f=0, so t=0! ) Even if the loop is not rectangular, as long as it is flat: t = I A B sinf. N (area of loop) # of loops

Understanding: Torque B B I (2) I (1) Compare the torque on loop 1 and 2 which have identical area, and current. Area points out of page for both! f = 90 degrees 1) t1 > t2 2) t1 = t2 3) t1 < t2 t = I A B sinf

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

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

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

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

Understanding Increase Stay the Same Decrease F=ILB sin(q)) Suppose the magnetic field is reversed so that it now points OUT of the page instead of IN as shown in the figure. o o o o o o o o o o o o X X X X X X X X X X X v v Fm Fm To keep the bar moving at the same speed, the force supplied by the hand will have to: Increase Stay the Same Decrease F=ILB sin(q)) B and v still perpendicular (q=90), so F=ILB 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. o o o o o o o o o o o o X X X X X X X X X X X v v Fm Fm To keep the bar moving to the right, the hand will have to supply a force in the opposite direction. True False Current flows in the opposite direction, so force direction from the B field remains the same!

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.

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

Induced Current 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.

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

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

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