phys 122 final

analyzing AC circuits

1) constrcutor phasor diagram 2) find the impedance 3) determine amplitude of current use: I=Emax/Z to find the phase of the current relative to the emf use: tan(theta)=[wL-(1/wC)]/R 4) find amplitude of potential difference across any reactive element using V=XI where X is the reactance

calculating inductance

1) find magnitude of magnetic field (through the loop or in the device) as a function of current 2) calculate the magnetic flux through the loop (if equation from step one depends on position= integrate) 3) take the derivative of the flux equation and set it equal to L(dI/dt) *******dI/dt should end up on both sides of this new equation 4) solve for L after eliminating dI/dt

calculating magnetic filed using amp's law

1) use right hand current rule to draw in magnetic field lines 2) if the field lines form circles the amp path should be a circle, if the lines are straight the amp path should be rectangular 3) make an amp path so that the field is perpendicular or tangent to the path. Make the part of the path that is parallel to the field in the same direction as the field. 4) use the right hand current rule to find the direction of the field of each current encircled by the path. If this field and the amp path have the smae direction, the Ienc is positive. 5) Calculate the line integral for each amp path. Express answer in terms of unknown B magnitude 6) use amp's law to relate Ienc and the line integral to solve for B.

from the cylindrical symmetry of the wire, the magnitude of the magnetic field decreases as...

1/r with distance r from the wire

electric field vs. magnetic field

E field= charged particle/changing magnetic field, exerts force on any charged particle B field= moving charged particle/changing electric field, exerts force on a moving charged particle

if a conducting loop or square move through a magnetic field what is established?

a current

if a wire carrying a constant current is bent into a loop...

all field lines inside the loop point in the same direction, reinforcing one another.

magnetic flux through a closed surface is...

always zero because field lines form loops

a changing magnetic field is accompanied by..

an electric field

a spinning charged particle has a magnetic field identical to that of...

an infantinitesimally small magnetic dipole

the integral along the noncircular path is eual to that along...

any circular path centered on the wire

why do kinks arise in electric fields?

because the field cannot change instantaneously everywhere in space to reflect changes in the source particle's motion

magnetic interactions

between magnets, current carrying wires, and moving charged particles

theta less than 0 in RLC (below resonance)

capacitor procides the dominant contribution to impedance and the current leads the emf

magnetic field between the plates of the charging capacitor arises from the...

changing electric field

when a conducting rod moves through a magentic field where velocity is perpendicular to magnetic field what is established?

charge separation

harmonic electromagnetic wave

charged particle oscillates sinusodially

there is a magnetic field in and around the gap between the plates of a...

charging capacitor

electromagnetic waves

combined disturbance in an electric and magnetic field that is propagating through space. kinks are electromagnetic wave pulses

planar electromagnetic wave

constant magnitude of the electric field in a plane normal to the direction of propagation uniform magnetic and electric field perpendicular to each other and to the direction of propagation

phasor rotates...

counnter clockwise

E cross B yields a vector in the direction of propagation (RHR)

curl fingers from E to B and thumb points in direction of propagation

VR is in phase with...

current

amperian path

current encircled by a closed path

when a loop moves into or out of a uniform magnetic field...

current is induced

given graph of emf for a non sinusodal AC circuit, graph current

current is the slope of emf times capcitance

work must be done on an inductor to establish...

current through it because the change in teh current causes an induced emf that opposes this change

magnetic dipole moment

defined to point like a compass needle along the direction of the magnetic field through the center of the dipole use right hand rule to find direction -curl your fingers along the direction of the current -thumb points in the direction

there can't be conventional current in a _______

dielectric

eddy currents

dissipate energy circular currents induced throughout the surface of the object

stationary charged particles

do not have magnetic interactions

inserting a dielectric increases the magnitude of the _______ between the plates of a capacitor, but the _______ surrounding the wires that lead to the capacitor is determined only by the _______ and cannot be affected by the insertion of a dielectric

electric field magnetic field current

polarization of waves

electric field of an electromagnetic wave as seen by an observer looking in the direction of propagation

when the current through a conducting loop changes, the changes induce an...

emf in the loop itself

AC circuits current is not proportional to.....

emf of the source

induced emfs

emfs produced by electromagnetic induction

As an electromagnetic wave travels _________ travels with it in the direction of ___________

energy propagation

length of phasor

equals amplitude

if you shrink the size of both the current loop and the bar magent, their magnetic field patterns become...

identical

the value of the line integral of the magnetic field along a closed path encircling a current-carrying wire is...

idependent of the shape of the path

the faster the current changes the greater the...

induced emf

a changing magnetic flux through a conducting loop...

induces a current in the loop

theta more than 0 in RLC (above resonance)

inductor dominates and the curren lags the emf

LC circuit

inductor in series with capacitor capacitor discharges more slowly than it would without the inductor when the capacitor is completely discharged all of the enery is contained in the magnetic field, and the current in the inductor is at a max current charges capacitor in opposite direction when current is zero and magnetic field are zero the capacitor is fully recharged in the oppose direction energy is constant UB+UE=U

finding magnetic field due to current

integration path should be taken along the path followed by the current. use biot-savart law

the current encircled by a closed path is equal to the current that is...

intercepted by any surface that spans the path not true for capacitors

magnetic flux through a closed surface

is always zero

the magnitude of the electric field in the kinks

is greater than everywhere else in the field

in an AC circuit that contains an inductor the current in the inductor _____ the potential difference by _____

lags, 90 degrees

In an AC circuit that contains a capacitor, the current in the capcitor ______ the potential difference by ____

leads, 90 degress (1/4 cycle)

light and electromagnetic wave relationship

light is an electromagnetic wave

biot-savart law

long straigh current carrying wire with a constant current dBs direction of dBs is curl fingers from dl to rsp and thumb will point in dBs

soleniod

long tightly wound helical coil of wire. generates strong magnetic field directed along the axis

electric field lines that accompany a changing magnetic field form...

loops

when the magentic dipole moment is parallel to the magnetic field all four sides of the loop experience

magnetic force, but the vector sum is zero and there is no torque

Vc

maximum value of an osicllating quantity (amplitude) maximum potential difference across a capacitor

power factor

measure of efficiency with which the source delivers energy to the load. when current and emf are in pashe max power is deilvered to the load

reactance

measure of the oppositiion of a circuit element to a change in current

field lines near the line of travel vs. in the plane perpendicular to the motion

near the line of travel= sparse perpendicular to the motion= closely clustered together

when a loop is entirely in or out of a magnetic field...

no current is induced

in a stationary loop next to a moving magnet...

no magnetic force is exerted on the loop, but a current is induced.

the magnetic field in a toroid is...

not constant, it depends on the distance r to the axis through the center of the toroid.

inductance

of a current carryin device or loop is a measure of the emf induced in the device or loop when the current is changed. (depends only on the geometry of the device) proportionality between the emf and the rate of change of current

the direction of an induced current through a conducting loop is always such that the magnetic fluc produced by the induced current...

opposes the change in magnetic flux through the loop

induced current is always in the direction that...

opposes the motion or change that caused it

resonance curve

oscillating physical quanitity has a peaked angular frequency dependence tall sharp peak= little dissipation

magnetic field lines are similar to electric field line patterns, but...

perpendicular to it

dipole moment

points from negative to positive

When the capacitor is connected direction to the AC source, the time dependent ________ across the capacitor ____ equals the ________ of the AC source at any instant

potential difference, vc, emf

difference between emf and potential difference

potential difference= electrostatic interactions, not dependent on path emf= nonelectrostatic interactions, depends on path

impedance

property of entire load ohms depends on the frequency for any load that contains reactive elements

phase constant

represents the phase differene betweeen the source of emg and the current when current leads= negative when current lags= positive

RC circuit

resistor and capcitor in series with AC source

a current loop placed in a magnetic field tends to...

rotate to align the magnetic dipole with the field.

frequency of magnetic and electric fields

same frequency, in phase

damping

similar to resistance

torid

solenois is bent into a circle so that the two ends are connected

source

source that generates sinusodially alternating potential difference or current

the line integral of the magentic field along a closed path is proportional to...

the current encircled by the path

induced current

the current that arises from the motion of charged particles realtive tot he magnetic field

potential energy in an inductor comes from...

the current through it or the magnetic field that is caused by the current

the magnetic field inside the solenoid depends on...

the current through the windings and on the number of windings per unit length

the greater the rate of change of magnetic flux through the loop...

the greater the induced current

dielectrics inserted in capacitors do not change...

the magnetic field because they don't change the current

a force does no work when...

the point of application doesn't move, or the force is perpendicular to the motion

RLC circuit all of the energy elivered to the circuit is dissipated in...

the resistor

the line integral of the magnetic field of a straight current-carrying wire over any circular path center on the wire has...

the same value

instantaneous value of quantity represented by a rotating phasor

the vertical component of the phasor

the emf of a charge-separating device is ...

the work done per unit charge by non-electrostatic interactions in separating charge within the device.

if the magnetic field due to a segment is perpendicular to the amp path...

they do not contribute integral of B*dl=0

when a particle accelerates what happens to the electric field lines?

they form kinks that do not go away when it reaches a constant speed

right hand dipole rule

thumb in direction of B and fingers curl in direction of I

right hand current rule

thumb in the direction of current (also change in electric field direction), fingers curl in direction of magnetic field

current loop in magentic field experiences magentic forces on...

top and bottom sides but not on the vertical sides becuase they are parallel to the direction of the magnetic field force on top and bottom sides cause torque

as you move a conductor relative to a magnetic field the work you do...

transfers energy to the conductor, setting the charge carriers in motion creating an induced current

finding the sum of oscillating potential differences

use pythagorean theorem to sum the two phasor vectors A= sqrt(v1^2+v2^2) where A is the new amplitude and v1 and v2 are the original amplitudes then use tangent to find the angle between V1+V2 and V1 (theta) V1+V2= Asin(wt+theta)

vc and i

when Vc is max, i is zero, when I is max, vc is zero

as you move a charged particle around a closed path through an electrostatic field, the work done by the electrostatic field on the particle is...

zero

the line integral of the magnetic field along a closed path that does not encircle any current-carrying wire is...

zero

when a charged object is moved around a closed path in an electrostatic field the work done on it is...

zero

when a solenoid is infinitely long the magnetic field outside approaches...

zero