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## 19 April 2012

### Just The Facts: Magnetism for AP Physics B

I'm running an AP Physics B prep session in Lynchburg, Virginia in a couple of weeks.  I've been asked to discuss magnetism.

Of course I'll bring my demonstrations and practice questions.  But these will be merely confusing without students knowing the background facts.  So, I'll hand out a "just the facts" sheet to everyone for their reference during the demos and practice questions.  Afterwards, they can use this sheet for their own review.

What do you need to know about magnetism for the AP B exam?

I.                  Magnetic force on a charge or wire

The amount of force provided by a magnetic field on a charge is qvBsinq.
·         q is the charge of the particle in the field, measured in coulombs
·         v is the speed of the particle
·         B is the magnetic field, measured in tesla
·         q is the angle between the velocity and magnetic field, usually 90o

The amount of force by a magnetic field on a current-carrying wire is ILBsinq.
·         same definitions as above for B, q
·         I is the amount of current in the wire, measured in amps
·         L is the length of the wire inside the magnetic field

The direction of force provided by a magnetic field is given by the first right hand rule
·         Do NOT plug in negative signs to qvBsinq.
·         Point toward v (or I), curl fingers toward B, thumb is direction of force on a positive charge or a current-carrying wire
·         (flip the direction for a negative charge)
·         Magnetic force is always perpendicular to velocity; this generally gives circular motion for a charged particle in the magnetic field.

II.               What can produce a magnetic field?

A bar magnet can produce a magnetic field.
·         Its field points out of the north end, and into the south end.

A current carrying wire can produce a magnetic field.
·         Its field wraps around the wire.  To find which way the field wraps, point right thumb with current and curl fingers.
·         The magnitude of the field produced by a straight wire is (μ0/2π)(I/d).
·         Here I represents the current creating the field, and d is the distance from the wire.

III.           A changing magnetic flux can produce a voltage

Magnetic flux through a loop of wire, F, is defined as BA.
·         B is the amount of magnetic field
·         A is the area of the wire loop through which the magnetic field directly penetrates
·         The units of magnetic flux are T∙m2.
·         If the magnetic field is not straight through the wire loop, only use the component of the field that is straight through the loop.

Changing flux produces a voltage
·         This voltage is referred to as “induced emf,” e.
·         The equation for the amount of voltage induced is n ΔΦ/Δt .
·         n represents the number of wire loops.  Dt represents the time it took to change the flux.
·         The induced current in a wire of known resistance can be found using V = IR.

The direction of induced current is given by Lenz’s Law
·         Current must flow through a wire – thus, only two directions are even possible for an induced current.
·         Point right thumb in the direction of the magnetic field.
o   (If flux is increasing rather than decreasing, flip your thumb the other way.)
·         Curl your fingers; this is the direction of the induced current.

Special case: moving rectangular wire entering or leaving a magnetic field
·         The induced voltage in this special case is e = BLv
·         Here, B is the magnetic field, v is the speed of the wire
·         L represents the side of the rectangle that always stays completely in the field, not the side of the rectangle that is entering or leaving the field
·         If the wire isn’t entering or leaving the field, the induced voltage is zero because flux doesn’t change.