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Unformatted text preview: homework 17 – LEE, BENJAMIN – Due: Oct 13 2007, 4:00 am 1 Question 1, chap 30, sect 3. part 1 of 2 10 points A long piece of wire with a mass of 0 . 327 kg and a total length of 30 . 248 m is used to make a square coil with a side of 0 . 398 m. The coil is hinged along a horizontal side (the y axis), carries a 1 . 59 A current, and is placed in a magnetic field with a magnitude of 0 . 0262 T in the vertical direction along the z axis as shown in the figure below. The acceleration of gravity is 9 . 8 . z x θ B =0 . 0262T B =0 . 0262T i = 1 . 59 A y . 398 m . 3 9 8 m Determine the angle that the plane of the coil makes with the z axis when the coil is in equilibrium. Correct answer: 11 . 1227 ◦ (tolerance ± 1 %). Explanation: Let : L = 30 . 248 m , ℓ = 0 . 398 m , m = 0 . 327 kg , i = 1 . 59 A , and B = 0 . 0262 T . Look down the positive yaxis at the coil (that is, from the righthand side of the origi nal figure). μ θ φ B mg x z Let θ be the angle the plane of the loop makes with the z axis as shown. Then the angle the coil’s magnetic moment μ makes with the z axis is φ = 90 ◦ − θ ; e.g. , sin φ = cos θ and tan φ = cot θ . The number of turns in the loop is N = L circumference = 30 . 248 m 4 (0 . 398 m) = 19 . The torque about the zaxis due to gravity is τ g = vectorr × vector F = parenleftbigg ℓ 2 cos φ parenrightbigg mg , where ℓ is the length of each side of the square loop. This gravitational torque tends to ro tate the loop clockwise. The torque due to the magnetic force tends to rotate the loop counterclockwise about the zaxis and has magnitude τ m = N B I A sin φ . At equilibrium, τ m = τ g N B I ℓ 2 sin φ = mg ( ℓ cos φ ) 2 . homework 17 – LEE, BENJAMIN – Due: Oct 13 2007, 4:00 am 2 Thus tan φ = mg 2 N B I ℓ = (0 . 327 kg) (9 . 8) 2 (19) (0 . 0262 T) (1 . 59 A) (0 . 398 m) = 5 . 08638 . Since tan φ = tan(90 ◦ − θ ) = cot θ , the angle the loop makes with the z axis at equilibrium is θ = cot − 1 (5 . 08638) = 11 . 1227 ◦ ....
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This note was uploaded on 04/07/2008 for the course PHY 303K taught by Professor Turner during the Fall '07 term at A.T. Still University.
 Fall '07
 Turner
 Mass, Work

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