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Unformatted text preview: “1 H-JIII"; Physics 211 Feb. 6, 1996
FINAL EXAM Time 2 hours Part A 30 min.
29 marks A1)A small water droplet has a diameter of 4 pm. If it carries a charge of
12 e' , a)-what is the strength and direction of the uniform electric ﬁeld that will
just balance the gravitational force acting on the droplet? b)-If the magnitude of the electric ﬁeld is then increased to three times its
previous value, how will the droplet behave compared with its behavior in the total absence of the electric ﬁeld? Given: e = l.6><10'19 C, the density of
water is 1g/cm3, Take g=10 m/secz. 15 marks A2) A current of 2.00 A ﬂows in a copper wire of 1.00 mm2 cross section.
How long does it take an electron to travel 10 cm in this wire under these
circumstances ? (Assume that each Cu atom contributes one conduction electron). Pen: 8.92 g/cm3, Mmmok= 63.5 g/rnol. and NA= 6.02x1023. 15 marks
A3) A toroidal coil is wound with 4000 turns of wire. The average radius of the toroid is 10 cm and the diameter of the coils is 1.5 cm. A second coil of
400 turns is wound over the ﬁrst. a)- What emf is induced in the second coil if the current in the 4000—turns
coil is changed ,at a rate of 25 A/sec? b)- Discuss also the sense of this induced emf. Part B 30 min.
15 marks _ Bl)- An electron half-way between two ﬁxed protons on the x-axis, is in stable equilibrium and executes simple harmonic motion aﬁer a slight
__;d|isplacement along the y-axis. Find the restoring force on the electron and
, deduce its natural frequency in terms of its mass m and charge 6 and proton-proton separation d.
‘ i 15 marks
B2)- A cylindrical capacitor has radii a<b, length L, and carries a charge q. a)- Find an expression for its capacitance.
b)—Calculate the electrical energy storedl if a= 4. 4 mm, b= 5.0 mm,
L 5 Ocm“, q= 6.0 'uC and (41:80)" =9 x109 Nm2/C2. ’ 2t] niarks : , 839'- Four long parallel wires forming the corners of a square, side a, run ' I ' perpendicular to the page and carry equal currents i each into page . a)-‘, Find the magnetic ﬁeld E at one corner due to the currents at the other
corners. b)—Calculate the magnetic force per meter exerted by f? on the wire of that corner if i=2.0A,a=50 cm, p..=4nx10"’T.m/A . an,” a ........ a Part C 30 min.
15 marl-u C1)- Two identical raindrops, each carrying surplus electrons on its surface
to make a net charge -q on each, collide and form a single drop of larger size-
Before the collision, the characteristics of each drop are the following : a)
surface charge density 60 , b) electric ﬁeld E‘ D at the surface, c) electric
potential V0 at the surface ( where V5 0 at r = on). For the combined drop ,
ﬁnd these three quantities in terms of their original values. (Hint: use the fact
that the volume is conserved). 2__[_I__ marks
C2)- An (1 particle ( q= +2e, m= 4. 003 u) travels in a circular path of radius
4. 5 cm in a magnetic field with B— — 1.2T. Calculate a) its speed, b) its period of revolution, c) its kinetic energy in eV, and d) the potential
difference through which it would have to be accelerated td achieve this
energy. ( u =1.661x10 "“ g, e = 160x10" C) 15 marks C3)— At t *0, a source of emf, E = 500 V, is applied to a coil that has an
inductance of 0.80 H and a resistance of 30 Q. . a)— Find the energy stored in the magnetic ﬁeld when the current reaches half
its maximum value. b)-How long after the emf is connected does it take for the current to reach
this value? ' Part D 30 min. 16 marks
‘ Dl)- A uniform conducting sphere of radius (a) carries a charge (+q). It is placed at the center of a spherical conducting shell of inner radius (b) and
outer radius (c). The outer shell carries a charge of (-q). Find: a)- E(r) within the sphere ( r<a ). b)- E(r) between the sphere and the shell. ( a<r<b ). c)—E(r) outside the shell (r>c). d)— Determine the charges which will appear on the inner and outer surfaces
of the shell. 18 marks D2)- A 2500 Q resistor is connected in series With a 100 uF capacitor, a 100
V battery and a switch. The capacitor is initially uncharged. The switch is
closed at t = 0. At what rate is the battery delivering energy to the circuit
at t= 0.5 sec ? Ml!
D3)- A solenoid with 1000 turns per meter has an iron core with the magnetization curve shown in the ﬁgure below. For a B0 ﬁeld of 1.2><10'3 T
(p() = 41tx10'7 N/Az): a)- Estimate the permeability constant Km 7 b)-Determine the current through the windings of the solenoid. 12| B0 in units of 210'4 T ...
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