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1. Using a dip needle, it is determined that the Earth's magnetic field makes an angle a with
respect to the horizontal plane. Then using a horizontal compass, a circular coil with N turns and
radius R is aligned with its plane vertical and its axis perpendicular to the horizontal component
of the Earth's magnetic field. The compass is placed at the center of the coil. Passing a current I
through the coil produces a deflection e in the direction of the compass needle.
a) Express the strength BEofthe Earth's magnetic field in terms of the current I, the angles a and
e, and the properties of the coil.
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2. Recall the can-crusher demonstration in which the charge stored by a large capacitor is rapidly
discharged through a conducting band around the middle of a soda can. Suppose that the current
flows in a counterclockwise direction within the plane of this page.
a) Sketch the discharge current and indicate the direction of the magnetic field it produces.
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3. A thick metal bar of mass m, length L, and resistance R slides without friction on a pair of
parallel metal rails with negligible resistance. The rod is initially at rest and the switch is closed
at t = O. The rails are connected to a battery that provides constant electromotive force &. A
uniform magnetic field B is directed perpendicular to the plane of the circuit formed by the rod
and rails. Show that the velocity Ofthe rod as a function of time takes the form v = v"" (1- e-t/r)
and determine v"" and T.
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4a) Two long perpendicular wires carrying equal currents cross, as shown, but do not quite
touch. Indicate on the diagram the locus of points at which the net magnetic field vanishes and
explain your reasoning.
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(ii) Under what conditions will v remain constant?
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5. A long cylindrical shell with inner radius a and outer radius b carries total current] along its
length.
a) Find expressions for the magnetic field in the regions (i) r < a, (ii) a < r < b, and (iii) r > b .
Sketch the function B(r) .
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