Magnetism

Question 1

Equation (p5) for the element of force dF on an element of current-length Idl in a magnetic field dB:

Answer 1

Question 2

Magnetic flux (p8) is the sum over an area of the density of magnetic flux through that area:

Answer 2

Question 3

The Lorentz force (p14) on a particle with charge q moving with velocity v in electric E and magnetic B fields:

Answer 3

Question 4

Hall effect (p18): magnetic Lorentz force on charge carriers carrying a current in a magnetic field leads to Hall voltage:

Answer 4

Question 5

Torque on a current loop (p27) of vector area A = Anˆ carrying current I in magnetic field B:

Answer 5

Question 6

The Biot-Savart Law (p33) for the element of magnetic field dB at distance r from currentlength element Ids:

Answer 6

Question 7

Standard results derived from Biot-Savart Law: (a) field of a current-carrying long straight wire (p35):

Answer 7

Question 8

Standard results derived from Biot-Savart Law:

field of a current carrying circular loop (on axis) (p41)

Answer 8

Question 9

Magnetic force between current carrying wires (p49):

Answer 9

Question 10

Amp´ere’s Law (p50):

Answer 10

Question 11

Standard results derived from Amp´ere’s Law (a) field of a current-carrying long straight wire (p51):

Answer 11

Question 12

Standard results derived from Amp´ere’s Law (b) field of a solenoid

Answer 12

Question 13

Standard results derived from Amp´ere’s Law

field of a toroid

Answer 13

Question 14

Magnetic field of an infinite conducting sheet:

Answer 14

Question 15

Definition of magnetic susceptibility (p3), χm in terms of applied field B0 and induced field Bm:

Answer 15

Question 16

Defintion of relative permability (p3, p24), µr in terms of total field inside material:

Answer 16

Question 17

Classification of magnetic materials (p3):

Answer 17

Question 18

Langevin paramegnetic equation (p13) for magnetization:

Answer 18

Question 19

Curie’s Law (p13) for small magnetic fields or large temperatures:

Answer 19

Question 20

Magnetization of ferromagnetic materials (p18):

Answer 20

Question 21

Magnetic intensity definitions (p19):

Answer 21

Question 22

Continuity at an interface between media (p21):

Answer 22

Question 23

Contributions from free and bound currents (p25):

Answer 23

Question 24

Gauss’ Law for magnetism (p9)in differential form:

and in integral form

Answer 24

Question 25

Boundary conditions on B and H (p15):

Answer 25

Question 26

Stokes’ Theorem (p19):

Answer 26

Question 27

The Amp´ere-Maxwell Law in integral form (p20):

Answer 27

Question 28

The Amp´ere-Maxwell Law in differential form (p26):

Answer 28

Question 29

Faraday’s Law for induced emf (electromotance) (p29):

Answer 29

Question 30

Self-inductance (p42): the induced back enf is proportional to the rate of change of current

Answer 30

Question 31

RL circuit (p45): behaviour after switch is closed. By applying Kirchhoff’s loop rule:

Answer 31

Question 32

Energy density in a magnetic field (p49):

Answer 32

Question 33

LC circuit (p52): (zero resistance ⇒ zero damping) charge on capacitor oscillates at angular frequenc

Answer 33

Question 34

Damped oscillations in RLC circuit (p57): resistance introduces damping

Answer 34

Question 35

Phasors (p9):

Answer 35

Question 36

Phasors in ac circuits (p9):

Answer 36

Question 37

Complex number representation (p16):

Answer 37

Question 38

RLC circuit complex impedance (p18):

Answer 38

Question 39

RLC circuit at resonance, ω = ω0 (p20):

Answer 39

Question 40

Average power in RLC circuit (p30):

Answer 40

Question 41

Resonance in RLC circuit (p32):

Answer 41

Question 42

Q-factor (p32):

Answer 42

Question 43

Maxwell’s equations in differential and integral form (p4):

Answer 43

Question 44

The wave equation in free space (p6):

Answer 44

Question 45

The Poynting vector represents the flux of energy density in the wave (p8):

Answer 45

Question 46

Average energy density passing a plane is the intensity or irradiance (p9):

Answer 46