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This was just a "trick question?" the professor told us on friday. Its not homework but he said "think about it on the weekend"

and I've been thinking about it!

http://img502.imageshack.us/img502/4705/harborloopjpg.jpg [Broken]

http://img502.imageshack.us/img502/4705/harborloopjpg.jpg [Broken]

A toroid keeps its magnetic field inside the coils, therefore in the middle of the toroid there wouldn’t be a magnetic field. If the toroid’s radius is larger than the dept of the harbor loop and the submarine is submerged, the loop would be inside the torid’s inner radius in which there is no magnetic field. The submarine would pass undetected by the loop. The submarine can be seen if its floating instead of submerged (a person could see it).

And this is what i was thinking, I emailed him but he told me "Your answer involves a rather extreme assumption -- one extreme enough to ensure that your answer is not a complete answer."

then I was thinking and tirpping out and came up with random stuff:

Taking into consideration the "width" of the loop, maybe assuming that its much larger (or at least as large) as the toroid's radius. Assuming the toroid's field does pass trough the harbor loop

If the magnetic flux is zero, there is no induced current. The magnetic flux is given by the dot product of B with dA, if they are perfectly perpendicular then theta would be π/2 therefore giving a zero flux. The submarine can't pass undetected due to the shape of the rectangular loop. If the toroid is perfectly aligned with the "horizontal" components of the loop at a right angle, the flux would be zero (since it's a dot product and the scalar version has a cosθ) Only the component parallel to the field would be detected. This can be avoided if the toroid's field is aligned with the earth's magnetic field and is the same magnitude as the earths magnetic field. The current is induced by a change of magnetic flux, if the fields are the same then there is no change in flux, the horizontal components would cancel due to the dot product and the other components would cancel if it were aligned to the earth's magnetic field.

and I've been thinking about it!

Here is my drawing:A `harbor loop' is a coil of wire of extensive area laid

out on the floor of a harbor entrance to detect the en-

trance of submarines by means of the voltage induced

by the submarine's natural magnetism. Suppose the

submarine is prolate in shape, and the submarine's

magnetic field happens to be the same as that of a

giant toroid, with the axis of the toroid along the axis

of the submarine and the radius of the toroid much

larger than the radius of the submarine. Further sup-

pose that the radius of the toroid is larger than the

depth of water above the harbor loop. If the harbor

loop is rectangular, is it possible for the submarine

to enter the harbor undetected? If so, under what

conditions? If not, why not?

http://img502.imageshack.us/img502/4705/harborloopjpg.jpg [Broken]

http://img502.imageshack.us/img502/4705/harborloopjpg.jpg [Broken]

A toroid keeps its magnetic field inside the coils, therefore in the middle of the toroid there wouldn’t be a magnetic field. If the toroid’s radius is larger than the dept of the harbor loop and the submarine is submerged, the loop would be inside the torid’s inner radius in which there is no magnetic field. The submarine would pass undetected by the loop. The submarine can be seen if its floating instead of submerged (a person could see it).

And this is what i was thinking, I emailed him but he told me "Your answer involves a rather extreme assumption -- one extreme enough to ensure that your answer is not a complete answer."

then I was thinking and tirpping out and came up with random stuff:

Taking into consideration the "width" of the loop, maybe assuming that its much larger (or at least as large) as the toroid's radius. Assuming the toroid's field does pass trough the harbor loop

If the magnetic flux is zero, there is no induced current. The magnetic flux is given by the dot product of B with dA, if they are perfectly perpendicular then theta would be π/2 therefore giving a zero flux. The submarine can't pass undetected due to the shape of the rectangular loop. If the toroid is perfectly aligned with the "horizontal" components of the loop at a right angle, the flux would be zero (since it's a dot product and the scalar version has a cosθ) Only the component parallel to the field would be detected. This can be avoided if the toroid's field is aligned with the earth's magnetic field and is the same magnitude as the earths magnetic field. The current is induced by a change of magnetic flux, if the fields are the same then there is no change in flux, the horizontal components would cancel due to the dot product and the other components would cancel if it were aligned to the earth's magnetic field.

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