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Unformatted text preview: Problem 1 (15 points) The switch in the circuit below has been open for a long, long time. Determine the currents [1,12,13 in the resistors and in the self—inductor at the moment
a. the switch is closed,
b. a long time after the switch is closed. The internal resistance of the battery is negligibly small. Express your answers ONLY in
terms of V, R1, R2 and L. Problem 2 (12 points) A current I goes through a rectangular wire in the direction shown with arrows in the ﬁgure.
The dimensions of the rectangle are a and b as shown. A uniform magnetic ﬁeld of strength
B is in a direction perpendicular to the paper (it’s coming towards you), as shown. What is
the torque on the rectangular 100p? QQQG Problem 3 (15 points) A mass spectrometer accelerates doubly ionized atoms of charge 26 over a potential difference
V before they enter a uniform magnetic ﬁeld B which is perpendicular to the direction of
motion of the ions. If d is the radius of the ions’ path in the magnetic ﬁeld, what is the mass
M of one ion? Express your answer ONLY in terms of V, B, e and d. The potential V is low
enough that no relativistic corrections are needed. Problem 4 (12 points) Apply Faraday’s law to show that a static electric ﬁeld between the plates of a parallel—plate
capacitor cannot drop abruptly to zero at the edges of the capacitor. Problem 5 (15 points) A current of I Amperes runs through a very, very long wire of which a portion (ACD) is
shown below. The direction of the current is indicated. The angle at C is 90°. CA is straight,
and it continues beyond A to the far left. CD is also straight and continues far beyond D. P
is a distance d meters from C; ACP is a straight line. What is the magnetic ﬁeld in Tesla
at P (magnitude and direction)? Hint: This problem can be done quickly without
complicated math. A I CdP Problem 6 (15 points) Two voltmeters, Vright and Vleft, each with an internal resistance of 106 Q are connected
through wires of negligible resistance (see the circuit below). The “+” side of both voltmeters
is up as shown. A changing magnetic ﬁeld is present in the shaded area. At a particular
moment in time Vright reads —0.1 Volt (notice the — sign). a. What, at that moment, is the induced EMF (in Volts) in the circuit? b. At that moment in time, what is the reading of Vleft? Problem 7 (16 points) A conducting bar of length D rotates with angular frequency to about a pivot P at one end
of the bar (see the ﬁgure). The other end of the bar is in slipping contact with a stationary
conducting wire in the shape of a circle (we only show a small part of that circle to keep the
drawing simple). Between point P and the circular wire there is a resistor R as shown. Thus
the bar, the resistor and the arc form a closed conducting loop. The resistance of the bar and
the circular wire are negligibly small. There is a uniform magnetic ﬁeld B everywhere, it
is perpendicular to the plane of the paper as indicated. What is the induced current in the loop? Express your answer in terms of D, to, R, and B. <0 869 ...
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 Spring '08
 Turner
 Physics

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