March 22, 2005 Physics for Scientists&Engineers 2 1Physics for Scientists &Physics for Scientists &EngineersEngineers 22Spring Semester 2005Lecture 33Midterm 2 ReviewMarch 22, 2005 Physics for Scientists&Engineers 2 2ReviewReview! Electric current i is the net charge passing a given point ina given time! The ampere is abbreviated as A and is given by! The current per unit area flowing through a conductor isthe current densityi =dqdt1 A =1 C1 s !JMarch 22, 2005 Physics for Scientists&Engineers 2 3Review (2)Review (2)! If the current is constant and perpendicular to thesurface, then and we can write an expression for themagnitude of the current density! The current density and the drift velocity are parallelvectors, pointing in the same direction, and we can write! The property of a material that describes its ability toconduct electric currents is called the resistivity, !J =iA !J = ne( )!vdMarch 22, 2005 Physics for Scientists&Engineers 2 4Review (3)Review (3)! The property of a particular device or object thatdescribes it ability to conduct electric currents iscalled the resistance, R! The resistance R of that conductor is define as! The unit of resistance is the ohm, !R =Vi1 ! =1 V1 AMarch 22, 2005 Physics for Scientists&Engineers 2 5Review (4)Review (4)! The resistance R of a device is given by•! is resistivity of the material from which the device is constructed•L is the length of the device•A is the cross sectional area of the device! The temperature dependence of the resistivity of metals is given by•! is the resistivity at temperature T•!0 is the resistivity at temperature T0•" is the temperature coefficient of electric resistivity for the materialunder considerationR =!LA!"!0=!0#T " T0( )March 22, 2005 Physics for Scientists&Engineers 2 6Review (5)Review (5)! The temperature dependence of the resistance of metals is given by•R is the resistance at temperature T•R is the resistance at temperature T0•" is the temperature coefficient of electric resistivity for the materialunder consideration! Ohm’s Law for a circuit consisting of a resistor and a battery is given by•Vemf is the emf or voltage produced by the battery•i is the current•R is the resistance of the resistorR ! R0= R0"T ! T0( )Vemf= iRMarch 22, 2005 Physics for Scientists&Engineers 2 7Review (6)Review (6)! We can visualize a circuit with a battery and a resistor inthree dimensionsMarch 22, 2005 Physics for Scientists&Engineers 2 8ReviewReview (7)(7)!n resistors in series can be replaced by an equivalent resistance givenby the sum of the resistances of the resistors in series!n resistors in parallel can be replaced by an equivalent resistance givenby the sum of the resistances of the resistors in parallel! The power dissipated in a circuit or circuit element is given byReq= Rii =1n!1Req=1Rii =1n!P = iV = i2R =V2RMarch 22, 2005 Physics for Scientists&Engineers 2 9Review (8)Review (8)! The force that a magnetic field exerts on a chargemoving with velocity v is given by! The magnitude of the forceexerted by a magnetic field ona moving charge is! If the charge moves perpendicular to the magneticfield then !FB= q!v !!BFB= qvBsin!F = qvBMarch 22, 2005 Physics for Scientists&Engineers 2 10Review (9)Review (9)! The unit of magnetic field strength the tesla (T)! Another unit of magnetic field strength that is often usedbut is not an SI unit is the gauss (G)! Typically the Earth’s magnetic field is about 0.5 G at thesurface! The NSCL K1200 superconducting cyclotron has a magneticfield of 5.5 T1 T = 1 NsCm= 1NAm1 G = 10-4 T10 kG = 1 TMarch 22, 2005 Physics for Scientists&Engineers 2 11Review (10)Review (10)! A charged particle with charge q and mass m moving withspeed v perpendicular to a constant magnetic field withmagnitude B will travel in a circle with radius r given by! For the same conditions we can relate the momentum pand the charge q to the magnitude of the magnetic fieldB and the radius r of the circular motionr =mvqBBr =pqMarch 22, 2005 Physics for Scientists&Engineers 2 12! If we run a current i through aconductor of width h in a constantmagnetic field B, we induce avoltage VH across the conductorthat is given by! where n is the number of electrons per unit volume and eis the charge of an electron! Hall EffectReview (11)Review (11)B =VHdv=VHdhnedi=VHhneiMarch 22, 2005 Physics for Scientists&Engineers 2 13Review (12)Review (12)!µ0 is the magnetic permeability of free space whose value is! The magnitude of the magnetic field at a distance r from along, straight wire carrying currrent i is given by! The magnitude of the magnetic field at the center of a loopwith radius R carrying current i is given byµ0= 4!"10#7 TmAB(r) =µ0i2!rB =µ0i2RMarch 22, 2005 Physics for Scientists&Engineers 2 14Review (13)Review (13)! Ampere’s Law is! where the integral is carried out around an Amperian loopand ienc is the current enclosed by the loop! The magnitude of the magnetic field inside a long wire withradius R carrying a current i at a radius r" is given by !B ! d!s""=µ0iencB(r!) =µ0i2"R2#$%&'(r!March 22, 2005 Physics for Scientists&Engineers 2 15Review (14)Review (14)! The force between two current-carrying wires is given by! The torque exerted by a magneticfield on a current-carrying loop isgiven byF12=µ0i1i2L2!d!= iAB sin"March 22, 2005 Physics for Scientists&Engineers 2 16Review (15)Review (15)! We define the magnitude of the magnetic dipole momentof a coil to be! We can express the torque on a coil in amagnetic field as! The magnetic potential energy of a magnetic dipole in amagnetic field is given byµ= NiA !!=!µ"!B !µ !ni U = !!µ"!B = !µB cos#March 22, 2005 Physics for Scientists&Engineers 2 17Review (16)Review (16)! The magnetic field inside an ideal solenoid is givenby! The magnetic field inside an ideal toroidal magnetis given byB =µ0inB =µ0Ni2!rMarch 22, 2005 Physics for Scientists&Engineers 2 18Review (17)Review (17)! Faraday’s Law of Induction in words is•The magnitude of the Vemf induced in a conducting loop is equal tothe time rate of change of the magnetic flux from the loop. Thisinduced emf tends to oppose the flux change.! Faraday’s Law of Induction in equation form is•Vemf is the induced voltage•d$B/dt is time rate change of the magnetic flux• The negative sign means that the induced voltage opposes thechange in fluxVemf= !d"BdtMarch 22, 2005 Physics for Scientists&Engineers 2 19Review (18)Review (18)! If we have a flat loop, we can keep two of the
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