Electricity and Magnetism - Department of Physics & Astronomy

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44. Consider the thick hemispherical shell of inner radius a and outer radius b, shownin cross section in the accompanying figure. If the shell is uniformly magnetizedalong its axis of symmetry (z – axis of the diagram), show that a small compassneedle placed at the origin will swing freely.45 Consider a rectangular piece of dielectric that fills the space between the plates,partially inserted into a plane – parallel condensor. What are the energies of thesystem as a function of position, and hence the forces drawing the dielectric intothe condensor, if the condensor plates are (a) insulated or (b) held at constantpotential?46. A spherical conducting shell occupies the region a < r < b. Find the fieldeverywhere, assuming that:
a) A point charge q is in the interior (r < a) of the shell at a distance d < a from thecenter.b) A point charge q is outside of the shell at a distance d > b from the center.c) A point outside a hollow conducting sphere will produce no field in the hollowinterior; the metal “shields” the interior. The solution to (a) shows that a pointcharge inside the hollow interior will produce a field outside; the same metalceases to act as a “shield”. Explain.47. Two similar charges are placed a distance 2b apart. A grounded conducting sphereis place midway between them. What radius (approximated within 1%) must theconducting sphere have in order to neutralize the mutual repulsion of the twocharges?48. A moving positron annihilates an electron at rest. Two photons are emitted. M isthe mass of the electron and positron, and ω 1 and ω 2 are energies of the twophotons. Show that:Cosφ =1− m ω 1− m ω 2,a) The angle φ between the two photons is given by,b) If one photon moves in the forward direction, the other photon must move inthe back ward direction.€49. Given the rate of radiation isdPdΩ = µ o q2 a 216π 2 csin 2 θ( 1− β cosθ) , 5where β = v/c, show that, for speed v close to c, θ max=( 1− β) /2 .€50. If a particle’s kinetic energy is n times € its rest energy, what is its speed v in terms ofn.
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Page 4 and 5: 8. Consider the following relativis
Page 6 and 7: 14. A square "loop" has been cut ou
Page 8 and 9: ) Both the field in the gap and the
Page 10 and 11: 25. A parallel plate capacitor has
Page 12 and 13: a) What is Cherenkov radiation and
Page 14 and 15: dz2 2Hint : ∫ = ln( z + z + d ).2

Electricity and Magnetism - Department of Physics & Astronomy

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