Assume the Earth\'s magnetic field is 50.8 T northward at 60.0° below the horizo
ID: 1790298 • Letter: A
Question
Assume the Earth's magnetic field is 50.8 T northward at 60.0° below the horizontal in a particular city. A tube in a neon sign stretches between two diagonally opposite corners of a shop window-which lies in a north-south vertical plane-and carries current 32.4 mA. The current enters the tube at the bottom south corner of the shop's window. It exits at the opposite corner, which is 1.49 m farther north and 0.850 m higher up. Between these two points, the glowing tube spells out DONUTS. Determine the total vector magnetic force on the tube. Hint: Two very important general statements are as follows. First, the force on the curved portion is the same in magnitude as the force on a straight wire between the same two points. In general, the magnetic force on a curved current- carrying wire in a uniform magnetic field is equal to that on a straight wire connecting the endpoints and carrying the same current Furthermore, F1 + F2 = 0 is also a general result: the net magnetic force acting on any closed current loop in a uniform magnetic field is zero. (Take east to be the +x-axis, up to be the +y-axis, and south to be the +z-axis.)Explanation / Answer
B = 50.8 uT (- cos60k - sin60j)
B = - 44 j - 25.4 k uT
IL = (32.4 x 10^-3) ( - 1.49k + 0.850 j)
IL = 0.0275 j - 0.0483k A m
F = IL X B
F = 2.13i + 0.6985 i
F = 2.823 i uN