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Unformatted text preview: Physics 211 September 2 , 1996 ic e artment ﬁnal Lg am Time2lzgggs r'r 1) l_0_u1_arks A certain charge Q is to be divided into two parts (Q—q) and q. What is the relation
of Q to q ifthe two parts, placed a given distranceppa‘rtzmaie‘t‘p have a maximum
Coulomb repulsion? “I” [rm] Filerv f!' I:l2ll:“'l  2) Lamas
A neutron is thought to be composed of one “up” quark of charge +§ e and two “dovvn” quarks each having charge e/3. If the down quarks are 2.6 F apart inside
the neutron, what is the repulsive electrical force between them? (i F = Fermi = 10"5m) ‘_3)I_5_marlss _ A charge per unit length of A is uniformly
distributed along the upper half of an inﬁnite
insulating rod and a charge per unit length of
J. is uniformly distributed along the lower half, _. as shown in the ﬁgure. Find the electric ﬁeld E
at P situated at a distance r from the point 0. 4) limarlss The spherical region a < r < b carries a charge per unit volume of p=A/r, where A
is a constant. At the center (r = 0) ofthe enclosed cavity is a point charge q. What
should be the value ofA so that the electric ﬁeld in the region a < r < b has constant
magnitude ? 5) images
Knowing that the potential in the space is given by V(x,y,z) = t; (x2 + yz) Where E_, a is a constant. Find the electric ﬁeld E and sketch the line ﬁelds in the space. 6)L0_matks Find the equivalent capacitance between a and b of the circuit shown where all the capacitors are identical. ‘ !
a ‘ I ‘ .b i. I Show that the plates of a parallelplate capacitor attract each other with a force
2 9’
28A 0 given by F = . Where q is the charge and A is the area of the plate. ' 8) ltharks
When 115 V is applied across a 9.66 m long wire, the current density is 1.42 A/mz.
Calculate the conductivity of the wire material. 4R 2R
9) iimarlss
Calculate the current i ifE = 12 V L
and R = 30. (llint, use AHY transformation). 3R ' SR
R
10) 15 marks 13 A long , rigid conductor, lying along the x axis, carries a current of 5.0 A in the
(x) direction. A magnetic ﬁeld B is present, given by I} = 3 2? + 8x232 , with x in meters and B in mT. Calculate the force on the 2.0 m segment of the conductor that
lies between x = 1.2 m and x x 3.2m. 11.) :5 marks ' . . Two long parallel wires a distance 2d
apart carry equal currents i in the same
direction, into the plane of the ﬁgure.
Derive an expression for the magnetic
field B at a point P on the line connecting
the wires and a distance x from the point
midway between them. Plot B against x. 12) i5.me 41/ .
a) Find an expression for the energy density as a function ofthe radial distance r
for a toroid ofrectangular cross section. [1) Integrating the energy density over the volume oftheiloroid, calculate the total
energy stored in the field of the toroid. ‘ ' 13) 15 marks
Consider the circuit shown: Describe qualitatively and quantitatively what happens if one of the switches is closed
and the other two switches are open , starting with switch 81 closed , then 82 and S}? 14) iimrlss
In an LC circuit with L = 52.2 mil and C = 4.21 ttF, the current is initially a . maximum. How long will it take before the capacitor is fully charged for the ﬁrst
time? 15) 1mm Which one of ihc following circuits resonate? What is its resonance frequency? 500 Q 5000 Q so
! goni ‘ §IOH J: . %1H
lmF '. OJmF lOmF Good Luck ...
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 Spring '10
 DimitriPolyakov
 Charge, Magnetism, Magnetic Field, Electric charge, Energy density

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