THE UNIVERSITY OF BRITISH COLUMBIA
 
Science 1 Physics Assignment # 6:
 
Faraday and Inductance
 
3 March 1999 - finish by 10 March

1.
Earth's-Field Generator:  What is the maximum that can be induced in a circular coil of 5000 turns and radius 50 cm by rotating it 30 times per second in the Earth's magnetic field in Vancouver ( $B = 5 \times 10^{-5}$ T)?

2.
Triangular Loop:  A wire loop in the shape of an equilateral triangle (length of a side $\ell = 0.25$ m) travelling at a constant speed v = 4.0 m/s moves, pointy-end first, into a region where a uniform magnetic field B = 0.50 T points into the paper, as shown.
\begin{figure}\begin{center}\mbox{ \epsfysize 1.75in \epsfbox{PS/triangular_loop.ps} } \end{center} \end{figure}
(a)
Does current flow clockwise or counterclockwise (or not at all) around the triangular loop as it enters the field?
(b)
What is the maximum induced around the loop as it enters the field?
(c)
Sketch the induced around the loop as a function of time, from the time it begins to enter the field until it is entirely in the field.

3.
Moving Loop in Non-Uniform Field:  A long, straight, stationary wire carries a constant current of i = 150 A. Nearby abcd, a square loop 12 cm on a side, is moving away from the stationary wire (in a direction perpendicular to the wire) at a speed of v = 6 m/s. The long wire and the sides of the loop are all in a common plane; the near (ab) and far (cd) sides of the loop are parallel to the long wire and the other two sides (bc and da) are perpendicular to it. The near side (ab) is initially $r_\circ = 15$ cm away from the long wire. Calculate the around the square loop at this instant, assuming that the resistance of the loop is large enough that any actual current flowing around it produces a negligible magnetic flux. Also indicate the direction of the small current in side cd.
\begin{figure}\begin{center}\mbox{ \epsfysize 2.0in \epsfbox{PS/loop_from_wire.ps} } \end{center} \end{figure}







4.
Dropping Frame: A square metallic frame is located, as shown, between the poles of an electromagnet, with its face perpendicular to $\Vec{B}$. The upper side is in a region of effectively uniform field with magnitude B = 1.5 T, while the lower side is outside the gap, where the field is essentially zero. If the frame is released and falls under its own weight, determine the downward terminal velocity. Assume the frame is made of aluminum (density 2.7 g/cm3 and resistivity $2.8 \times 10^{-6}$ $\Omega$-cm). This problem requires careful thought. It is interesting that the terminal speed can be found with so little information about the metallic frame.
\begin{figure}\begin{center}\mbox{ \epsfysize 1.6in \epsfbox{PS/dropping_frame.ps} } \end{center} \end{figure}


Jess H. Brewer
1999-03-03