- #1
Zack K
- 166
- 6
- Homework Statement
- A thin rectangular coil lies flat on a low-friction table. A very long straight wire also lies flat on the table, a distance ##z## from the coil. The wire carries a conventional current ##I## to the right as shown, and this current is decreasing: ##I=a-bt##, where##t## is the time in seconds, and ##a## and ##b## are positive constants. The coil has length ##L## and width , where ##w\ll z##. It has ##N## turns of wire with total resistance ##R##.(I uploaded an image)
What are the initial magnitude and direction of the nonzero net force that is acting on the coil? You can neglect friction. Explain in detail. If you must make simplifying assumptions, state clearly what they are, but bear in mind that the net force is not zero.
- Relevant Equations
- ##\oint {E \cdot d\ell = - \frac{d}{{dt}}} \int {B_n dA}##
##B_{wire}=\frac{\mu_0}{4\pi}\frac{LI}{z\sqrt{z^2+(\frac{L}{2})^2}}\longrightarrow B_{wire}=\frac{\mu_0}{4\pi}\frac{2I}{z}##(for ##z\ll L##)
I don't understand why a force would be acting on this rectangular coil at all. The magnetic field of the wire would only induce a force on the coil, if the coil had a current flowing through it. At first I would think that the electric field from the varying magnetic field would induce such current through the wire, but the electric field is going perpendicular to the length of the coil, which would not induce a current. The only thing that seems plausible is that the electric field causes the wire to be polarized along the thickness, but that obviously isn't right.
EDIT: I just realized I'm completely wrong, I think I get what's happening. The magnetic field is pointing into the page at the location of the wire and if the current\magnetic field is decreasing, then the electric field will go clockwise around the coil.
EDIT: I just realized I'm completely wrong, I think I get what's happening. The magnetic field is pointing into the page at the location of the wire and if the current\magnetic field is decreasing, then the electric field will go clockwise around the coil.