Magnetism & Electromagnetism AP Physics B

Facts about Magnetism Magnets have 2 poles (north and south) Like poles repel Unlike poles attract Magnets create a MAGNETIC FIELD around them

Magnetic Field A bar magnet has a magnetic field around it. This field is 3D in nature and often represented by lines LEAVING north and ENTERING south To define a magnetic field you need to understand the MAGNITUDE and DIRECTION We sometimes call the magnetic field a B-Field as the letter “B” is the SYMBOL for a magnetic field with the TESLA (T) as the unit. Magnetic fields are vectors!

Earth’s Magnetic Field Aurora Borealis (Australis) Occur when highly charged electrons from the solar wind interact with elements in the earth's atmosphere.

Magnetic Force on a Moving Charge (+)Particle is shot East in a magnetic field directed upward (North to South) The Direction: RHR predicts that the force on the particle will be directed out of the page along the z-axis. The resulting motion is a curved path. The Magnitude is given by the equation: Where, q is the + charge, v is the velocity, B is the magnetic field strength and θ is the angle between velocity and perpendicular of B field.

Direction of the magnetic force? Right Hand Rule To determine the DIRECTION of the force on a POSITIVE charge we use a special technique that helps us understand the 3D/perpendicular nature of magnetic fields. Basically you hold your right hand flat with your thumb perpendicular to the rest of your fingers The Fingers = Direction B-Field The Thumb = Direction of velocity The Palm = Direction of the Force For NEGATIVE charges use left hand!

Magnetic Force on a Moving Charge S B The conditions for the force are: Must have a magnetic field present Charge must be moving Charge must be positive or negative Charge must be moving PERPENDICULAR to the field or at θ from perpendicular. N S N vo - What is the direction for the magnetic force on the particle as it tries to enter the field? HINT: particle is (-), flip your hand! Out of the page(shown with dots) so the particle deflects toward us and curves out of the magnetic field

Give the direction of the magnetic force (+) y-axis or North (+)z-axis or Out of page No force, parallel

Magnetic Force and Circular Motion B v X X X X X X X X X - Suppose we have an electron traveling at a velocity , v, entering a magnetic field, B, directed into the page. What happens after the initial force acts on the charge? - FB FB FB - - FB - The magnetic force is equal to the centripetal force and thus can be used to solve for the circular path. Or, if the radius is known, could be used to solve for the MASS of the ion. This could be used to determine the material of the object. There are many “other” types of forces that can be set equal to the magnetic force. (if the B field accelerates: F=ma. If it levitates: F=mg)

Problem A singly charged positive ion has a mass of 2.5 x 10-26 kg. After being accelerated through a potential difference of 250 V, the ion enters a magnetic field of 0.5 T, in a direction perpendicular to the field. Calculate the radius of the path of the ion in the field. We need to solve for the velocity! 0.0177 m 56,568 m/s

Forces on Current-Carrying Wire Up to this point we have focused our attention on PARTICLES or CHARGES only. The charges could be moving together in a wire. Thus, if the wire had a CURRENT (moving charges), it too will experience a force when placed in a magnetic field. You simply used the RIGHT HAND ONLY and the thumb will represent the direction of the CURRENT instead of the velocity. Where θ is measured from perpendicular of B field

Problem A 36-m length wire carries a current of 22A. Calculate the magnitude and direction of the magnetic force acting on the wire if it is placed in a magnetic field with a magnitude of 0.50 x10-4 T and directed North along the (+) y-axis? I = 22A B = (+)y-axis - North I = (+)x-axis - East So. By the RHR: F = 0.0396 N (+)z-axis – out of the page

WHY does the wire move? The real question is WHY does the wire move? It is easy to say the EXTERNAL field moved it. But how can an external magnetic field FORCE the wire to move in a certain direction? THE WIRE ITSELF MUST BE MAGNETIC!!! In other words the wire has its own INTERNAL MAGNETIC FIELD that is attracted or repulsed by the EXTERNAL FIELD. As it turns out, the wire’s OWN internal magnetic field makes concentric circles round the wire. (Oersted)

A current carrying wire’s INTERNAL magnetic field To figure out the DIRECTION of this INTERNAL field you use the right hand rule. You point your thumb in the direction of the current then CURL your fingers. Your fingers will point in the direction of the magnetic field

The MAGNITUDE of Wire’s field The magnetic field, B, is directly proportional to the current, I, and inversely proportional to the circumference at a position, r, from the wire.

Problem A long, straight wires carries a current of 5.00A. At one instant, a proton, 4 mm from the wire travels at 1500m/s parallel to the wire and in the same direction as the current. Find the magnitude and direction of the magnetic force acting on the proton due to the field caused by the current carrying wire. v X X X 2.51 x 10- 4 T 4mm + 6.02 x 10- 20 N Direction for force on proton: B = out of the page (x) and v = North Then F = 5A West

Force between two current carrying wires Force on Wire 1 due to the B field of Wire 2:

Magnetic Field for Current Carrying Loops μo -permeability of free space r - the radius of the loop N – number of loops I – current through loop Magnetic Field AT THE CENTER: Example with only 1 loop, so N = 1: Solenoid with 4 loops, so N = 4: Also, Binside solenoid = μoI(N/L) If an iron core is added, these would be electromagnets!

RHR for Wire Loops Thumb points toward “North” of the B field

DC Motor The nail would rotate in the magnetic field along the pivot point providing mechanic energy….however, the wires would be hopelessly tangled….so… A commutator is used. It allows the wire coil to rotate by reversing the direction of current flow through the wire for each ½ rotation.

Electromagnetic Induction

Current is induced in the loop when the permanent magnet is MOVED Why does this happen? External Magnetic flux through the wire induces a magnetic field and therefore a current through the wire. http://www.cabrillo.edu/~jmccullough/Physics/Electromagnetic_Induction.html

Faraday’s Law Faraday learned that if you change any part of the flux, ΦB, over time you could induce a current in a conductor and thus create a source of EMF (voltage, potential difference). Since we are dealing with time here were a talking about the RATE of CHANGE of FLUX, which is called Faraday’s Law.

Practice Problem - Faraday A 500-turn rectangular loop of wire has an area per turn of 4.5 x 10-3 m2. at to=0s, a magnetic field is turned on and its magnitude increases to 0.50 T when t = 0.75 s. The field is directed at an angle, θ = 30.0o with respect to the normal of the loop. (a) Find the magnitude of the average emf induced in the loop. (b) If the loop is a closed circuit whose resistance is 6.0Ω , determine the average induced current.

Lenz’s Law An induced emf in a wire loop as a direction such that the current it creates produces its own magnetic field that opposes the change in the magnetic flux through that loop. Right hand rule (Pulling Out North Pole)

Lenz’s Law Lenz's law gives the direction of the induced emf and current resulting from electromagnetic induction. The law provides a physical interpretation of the choice of sign in Faraday's law of induction, indicating that the induced emf and the change in flux have opposite signs. In the figure above, we see that the direction of the current changes. Lenz’s Law helps us determine the DIRECTION of that current, I = V/R or ε/R in our case.

Lenz’s Law & Faraday’s Law Let’s consider a magnet with it’s north pole moving TOWARDS a conducting loop. DOES THE FLUX CHANGE? DOES THE FLUX INCREASE OR DECREASE? WHAT SIGN DOES THE “Δ” GIVE YOU IN FARADAY’S LAW? DOES LENZ’S LAW CANCEL OUT Yes! Increase Positive NO This means that the INDUCED MAGNETIC FIELD around the WIRE caused by the moving magnet OPPOSES the original magnetic field. Since the original B field is downward, the induced field is upward! We then use the curling right hand rule to determine the direction of the current.

Lenz’s Law & Faraday’s Law Let’s consider a magnet with it’s north pole moving AWAY. DOES THE FLUX CHANGE? DOES THE FLUX INCREASE OR DECREASE? WHAT SIGN DOES THE “Δ” GIVE YOU IN FARADAY’S LAW? DOES LENZ’S LAW CANCEL OUT Yes! Decrease Negative Yes (-)x(-)=(+) In this case, the induced field DOES NOT oppose the original and points in the same direction. Once again use your curled right hand rule to determine the DIRECTION of the current.

Lenz’s Law Demo The INDUCED current creates an INDUCED magnetic field of its own inside the conductor that opposes the original magnetic field. The induced current in the copper tube creates its own induced magnetic field that opposes the magnetic field that created it. A magnet is dropped down a conducting copper tube. The copper tube "sees" a changing magnetic field from the falling magnet. The magnet INDUCES a current in the copper tube above and below the magnet as it moves. And since the induced magnetic field opposes the direction of the original it attracts the magnet upward slowing the motion caused by gravity downward. Why does it fall slowly?

Practice Problem A long, straight wire lies on a table and carries a current I. As shown in the drawing below, a small circular loop of wire is pushed across the top of the table from position 1 to position 2. Determine the direction of the induced current, clockwise or counterclockwise, as the loop moves past position 1 and position 2. At position1, flux is increasing, so the induced magnetic field opposes the external field (around wire) which is out of the page

Practice Problem – Change in Strength The magnetic field point out of the screen and is increasing in magnitude at a constant rate. Is the direction of the current through R to the right or left? Since the magnetic field strength is increasing, the flux through the loop is increasing. The induced current will therefore flow in a direction that produces a magnetic field that opposes the external magnetic field which is out of the page. To produce a magnetic field that points into the page, the current must flow through R to the right.

Problems The rectangular loop is pushed into the magnetic field which points inward as shown. In what direction is the induced current flowing through the resistor R? Because it counteracts flux into the page by generating flux out, it's Counterclockwise The north pole of the magnet is being inserted into the coil.  In which direction is the induced current flowing through the resistor R? the current flows from right to left through the resistor

Problem The moving rod is 12.0 cm long and moves with a speed of 15.0 cm/s along the U shaped conductor with a uniform magnetic field pointing out of the page. If the magnetic field is 0.800 T, calculate the emf developed (b) the electric field in the rod. ε= Blv = (0.800T)(0.12m)(0.15m/s) = 0.0144 V E = vB = (0.15m/s) (0.800) = 0.12 V/m

Transformers AC Current from the primary coil moves quickly BACK and FORTH across the secondary coil. The moving magnetic field caused by the changing field (flux) induces a current in the secondary coil. A transformer can be: STEP UP or STEP DOWN.

Motional EMF http://www.ngsir.netfirms.com/englishhtm/Induction.htm