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APB Review Sessions
Magnetism and Induction

Magnetic fields are measured in Tesla - 1 T field exists when 1 meter of wire carrying 1 amp of current experiences 1 N of magnetism force.

B fields into the plane of the paper are represented by X
B fields out of the plane of the paper are represented by .

moving charges experience magnetic forces

F = q v B^ = q v B sin q

RHR - thumb points in direction of the positive particle's velocity, fingers in the direction of B^, and palm in the direction of the force

FB = FC that is, moving charges are forced into circular paths while traveling through magnetic fields - paths are usually described as cw or ccw

q v B^ = m ( v / r )

the time required for one revolution in these circular paths is independent of the particle's velocity

v = (2 p r) / T

the radius of the particle's circular path is directly proportional to the particles mv, and inversely proportional to the particle's charge and the strength of the magnetic field

both stationary and moving charges experience electric field forces
F = qE where E = V / d and can be measured in either N/C or V/m

particles are linearly accelerated through electric fields - "accelerating potential"

| q V | = mvf - mvo

velocity selectors are designed to permit similarly charged particles with an predetermined velocity travel in straight paths through crossed magnetic and electric fields

q v B^ = q E
v = E / B^

field lines run out of the N pole and into the S pole
like poles repel, unlike poles attract (similar to field diagrams for two point charges)

solenoids are electromagnets - Curl Rule - fingers curl in the direction of the current flowing through the coils, thumb points in the direction of the solenoids N pole (magnetic moment)

solenoids are important because they have uniform B fields along their axis

B = mo n I where mo = 4 p x 10-7 Tm/A and n = N / L

current carrying wires produce radial B fields

curl rule - thumb points along the wire in the direction of the current, fingers curl in the direction of the B field

B^ = 2 x 10-7 I / d

magnetic fields from neighboring wires can be superpositioned to find the net B in a region of a plane

current carrying wires experience forces when placed in external magnetic fields

F = B^ external I L

parallel wires carrying opposing currents repel
parallel wires carrying currents flowing in the same direction attract

galvanometers - sensitive current carrying coils rated for a maximum allowed current and voltage to produce a full scale deflection.

ammeter - place a low resistance shunt in parallel with the galvanometer as a path for the excess current

I main = I galvanometer + I shunt

shunt and galvanometer have the same voltage
remember that ammeters are USED in series to determine the current passing through a given resistor

voltmeter - place a high resistance multiplier in series with the galvanometer to bleed off the excess voltage

V total = V galvanometer + V multiplier

multiplier and galvanometer have the same current

remember that voltmeters are USED in parallel to determine the potential (voltage) lost across a given resistor

The formula used to calculate the number of magnetic flux (field) lines which pass through a given cross-sectional area is

F = B^ A
F is measured in webers, B^ is in T, A is in m
Note that these units define a Tesla as a weber/m.

When the number of flux lines is constant, no emf is induced in a coil. When you change the number of lines, an emf is generated in the coil opposing THE CHANGE.

Faraday's (Lenz) Law of Induction is E = - N (D F /Dt )

The expression D F /Dt = D (B^ A) / Dt is merely an abbreviation for the rate of change of flux lines. Notice, an emf is induced only when the number of flux lines passing through an enclosed area changes. This number can be changed by either changing the strength of the magnetic field OR by changing the area of the coil.

E = - N B^ (D  A /D t ) = - N B^ (A f – A o )/t
E = - N A (D  B^ /D t ) = - N A (B^f – B^o )/t

Also notice that the emf is induced to oppose these changes (designated by the negative sign). Your right-hand curl rule (your fingers will curl in the direction of the induced current when your thumb points in the direction of the coil’s induced magnetic moment or North Pole) is used to determine the direction of the induced emf/current.

The formula used to calculate the emf induced in a loop which has a changing cross-sectional area while present in a constant perpendicularly-oriented magnetic field, B^, is

Emotional = - N B^ v l

This occurs when a loop is pushed into or pulled out of a constant magnetic field or when a sliding conducting bar changed the enclosed area within a magnetic field. The right-hand curl rule was used to determine the direction of the induced emf/current.

The force that must be applied to maintain a constant velocity is calculated with the equation

Fright = B^IL
= B^ (E / R) L
= B^ (B^ v LR) L
= B^ v L R

The generalized equation for the operation of a motor is Electricity + Magnetism = Motion

When electricity is supplied to a coil and it is inserted within a permanent magnetic field, the two magnetic fields repel and attract each other causing the loop to rotate.

The generalized equation for a generator is Motion + Magnetism = Electricity

When a coil is rotated within a permanent external magnetic field, the changing flux lines generate a voltage within the coil. Since the coil has resistance, this induced emf will result in an induced electric current. The equation for the AC voltage generated in the coil is v = Vo sin (2pf)t where

Vo = NBA(2pf) and the frequency is in hz.

The Law of Transformers states that Ns / Np = Es / Ep where Np and Ns are the number of loops in the primary and secondary coils and Ep and Es are the emfs in the primary and secondary. A transformer only works when the number of flux lines through the iron core of the transformer keeps changing - therefore, the primary must be connected to an AC source. Any change in flux in the primary is communicated to the secondary through the iron core. The power utilized in both coils is the same!

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Catharine H. Colwell
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