A copper sheet with length 1.31 m, width 0.539 m, and thickness 1.01 mm is oriented so that its largest surface area is perpendicular to a magnetic field of strength 4.81 T. The sheet carries a current of 3.05 A across its length. a) What is the magnitude of the force on this sheet? b) What would the magnitude of the force on a thin 1.31-m-long copper wire be, if it carried the same current and was oriented perpendicularly to the same magnetic field?
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A current carrying conductor in a magnetic field will feel a force (the Laplace force). The magnitude of this force is given by FILxB, where L is a vector whose magnitude is the length of wire, and whose direction is along the wire, aligned with the direction of current flow I, and B is the magnetic field vector. This applies to a straight, rigid wire with a constant current in a uniform magnetic field. [ LxB is the vector cross product (product of the magnitudes of L and B and sine of the angle between them) ]. a) 19.2 N. F(3.05 A) x (1.31 m) x (4.81 T) x (sin90°) 19.2 N b) also 19.2 N. As long as all of the current is exposed to the magnetic field the net force is the same and it depends only on current, length, and field strength.
