Exam 3 Vocab

• (True or False) bar magnets behave as though the north and south poles are positive and negative "magnetic" charges

  True (but the charges are illusions)
• If a bar magnet's north end has magnetic charge qm=4000 Cm/s, what will be the force on that end of the magnet when it is placed in a field B=0.5 T k

  F=qmB=2000N k
• A 1 mg bar magnet with magnetic charge qm=+100 Cm/s at north and south ends respectively is placed in a uniform field B=0.5 T k. What is the force on the magnet?

  F=0; B is perpendicular with this bar magnet
• For the magnet above, if the vector d=3 cm i * 4 cm j connects the south pole to the north pole, what is the magnetic dipole moment?

  m=qmd= 100 cm/s * (0.03m i + 0.04m j) = 3 Am^2 i + 4 Am^2 j
• What is the torque on the bar magnet above?

  T=mxB = |i j k|

  |3 4 0|

  |0 0 .5|

  
  

  =(ix2-jx1.5)Nm
• Two pole faces of 1 mg permanent magnets are placed in proximity. The ends have equal and opposite magnetic charge densities. Sketch B.


  Field is nearly uniform (B=Mu-naught * sigma)
• South pole of magnet 1 is separated from south pole of magnet 2 by displacement r as shown. What is F on south pole of 2 due to south pole of 1?


  F= Mu-naught / 4pi * ((-qm1*-qm2)/|r|^2) r

  Coulomb's Law
• South pole of magnet 2 is butted up against north pole of magnet 1. If sigma1=1000 Cm/s/m^2 and sigma2=2000Cm/s/m^2, and surface area of pole faces is 1x10^-4 m^2, what is the force of attractions? (neglect interactions with opposite pole faces)


  F = (Mu-naught*sigma1/2) x (sigma2*A) = ((4pi*10^-7)(1000)(2000)(1x10^-4))/2 = (4pi/2)x10^-5 N (attractive)
• Write down the expression for the force on a charge q moving with velocity v in a magnetic field B

  F=qvxB
• Express Tesla in terms of their constants.

  1 T = (1 N / 1 C 1 m/s) = Ns/Cm
• What is the force F on an electron moving at 5x10^5 m/s i in a magnetic field of -2.5 T k?


  F = -(1.6x10^-19 C)(5x10^5)(2.5)(i x (-k)) = -20x10^-14 N j

  i x k = -j

  i x (-k) = +j
• What is the radius of curvature for a proton with speed 5x10^5 m/s moving in the x-y plane in a magnetic field B=1x10^-4 T k?

  qvB=mv^2/r

  r=mv/qB

  r = ((1.67x10^-27 kj)(5x10^5))/((1.6x10^-19)(1x10^-4)) = 5x20^(-27+5+19+4)=50m
• What is the frequency for a proton moving in a circle with a magnetic field of 1x10^-4 T?

  qvB=mv^2/r

  v/r=w=qB/m=((1.6x10^-19)(1x10^-21))/(1.67x10^—27) = 1x10^(-23+27)=1x10^4 rad/s

  f=(1x10^4)rad/s x 1 rev/2pi rad = 1.6x10^3 Hz
• What is the “cyclotronfrequency?


  the frequency for a charged particle to move in a circle in a uniform magnetic field: w=qB/m
• What is the most general motion for a charged particle in a uniform magnetic field?

  A helix. (component of V0 that is parallel to B is not deflected)
• Why is it said that a magnetic field can do no work on a charged particle?

  F=qvxB, so F is perpendicular to both v and B. Since the power P=F*v=0 (since F and v are perpendicular), there can be no work done
• Write down the expression referred to as “Gauss’s law for magnetism”. What does it imply?

  Integral (B * dA) = 0; closed surface

  no isolated magnetic “charges”… also said, “no magnetic monopoles”
• What is the strength of the Earth’s magnetic field at the surface of the Earth? (roughly)

  |B|=0.5 Gauss, (1 Gauss=10^-4 Tesla)
• What is the Van Allen belt?

  A layer of charged particles that is trapped by Earth’s magnetic field
• A segment of wire carrying current I in a magnetic field experiences a force. What will be the force in the most general case (when B depends on position)?

  F = Integral]1-2 of IdlxB
• How does this simplify if B is uniform in space?

  F=I (integral]1-2 of dl)xB = I * delta l x B
• What is force on top half of current-carrying wire ring for uniform B?

  F = (5A)(2m)(1 T) up-direction = 10 N up

  
• A segment of wire carrying a current of 5A begins at (1m, 0.5m, 3m) and ends at (2m, 1m, 2m) with current flowing from beginning to end. If B=5T k, what is F?


  F = I * delta l x B for uniform B.

  delta l = (2-1)m i + (1-1/2)m j + (2-3)m k = 1 m i + 0.5 m j - 1 m k

  F=(5A)[i(0.5)(5)-j(1)(5T)+k*0]

  F=12.5 N i - 25 N j
• What is the force on a closed loop circuit carrying a current I in a uniform B?

  F=I(integral of dl) x B = 0
• What is the torque on a closed-loop circuit in a uniform B?


  T = IA x B

  A = area of loop
• Which way does A point?

  Normal to area of loop, and in direction of I according to right-hand screw rule
• For the current loop in the x-y place shown, which way is

  A and what is its magnitude?

  A=(pi * r^2) k

  
• if B=2T j and r=1m and I=3A, what is T? Which way will loop twist?

  A = pi(1m)^2 k = pi*m^2 k

  T=(3A)(pi*m^2)*(2T)(k x j) —-> note: kxj= -i

  = -6*pi Nm i
• What direction is k? up or down?

  down

  
• What is T vs. rotation angle?

  T=IAB |sin theta|
• For a 5A current in a 1T field, what is the force on the “slidewire”?

  F = I * l x B = (5A)(1m)(1T)=5 N to the right
• What is the magnetic moment of a current loop with area A carrying current I?


  m = IA
• What is the torque on a magnetic moment in a magnetic field?

  T=mxB
• What is the alignment energy of a magnetic moment in a magnetic field?

  U=-m*B
• What is the Bohr magneton?

  Mbohr = eh/ 4*pi*me

  It is the magnitude of the magnetic moment of hydrogen due to the orbital motion of the electron if the electron were moving in a circular orbit at the first Bohr radius
• What is the name for the “intrinsic” angular momentum of an electron?

  “spin”
• What is the “magnetization” of a material?

  M = n<m>
• what is the magnetic susceptibility?

  m=XH

  The constant of proportionality between the “magnetic intensity” and the magnetization
• What is H?


  H=B/Mu-naught - m
• If x=1x10^-4 the material is…

  paramagnetic

  examples: Al, W, Li, Mg, Cs, Na