homework 4

# homework 4 - montes(dam2772 Homework4 shih(56310 This...

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montes (dam2772) – Homework4 – shih – (56310) 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0points Two long, parallel wires are separated by a distance 2 d , as shown below. Wire #1 carries a steady current I into the plane of the page while wire #2 carries a steady current I out of the page. d d P I I S S wire #2 wire #1 At what points in the plane of the page (besides points at infinity), is the magnetic field due to the currents zero? 1. At no points. correct 2. At only point P . 3. At all points on a circle of radius d cen- tered at either wire. 4. At all points on the line SS , a perpen- dicular bisector of a line connecting the two wires. 5. At all points on the line connecting the two wires. Explanation: The only way that the total magnetic field would be zero is if the magnetic fields due to the two wires have the same magnitude but opposite directions at the same point. Only at points on the line SS do the mag- netic fields have the same magnitude. Only at point P are the magnetic fields parallel (aligned with the vertical axis). Using the right hand rule, they are in the same direc- tions. Thus, at no points (besides points at infin- ity) is the magnetic field due to the currents zero. 002 10.0points A thin 1.32 m long copper rod in a uniform magnetic field has a mass of 58.1 g. When the rod carries a current of 0.213 A, it floats in the magnetic field. The acceleration of gravity is 9 . 81 m / s 2 . What is the field strength of the magnetic field? Correct answer: 2 . 02718 T. Explanation: Let : = 1 . 32 m , m = 58 . 1 g = 0 . 0581 kg , I = 0 . 213 A , and g = 9 . 81 m / s 2 . The magnetic and gravitational forces are equal: F m = F g B I ℓ = m g B = m g I ℓ = (0 . 0581 kg) (9 . 81 m / s 2 ) (0 . 213 A) (1 . 32 m) = 2 . 02718 T 003(part1of2)10.0points Given a current segment which flows along the edges of a cube as shown in the figure. The conventional Cartesian notation of ˆ ı (a unit vector along the positive x axis), ˆ (a unit vector along the positive y axis), and ˆ k (a unit vector along the positive z axis), is used. The cube has sides of length a . The current flows along the path A → C → D → E → G . There is a uniform magnetic field vector B = B ˆ k .

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montes (dam2772) – Homework4 – shih – (56310) 2 z x y B B B A C D E G a a Find the direction hatwide F vector F bardbl vector F bardbl of the resul- tant magnetic force on the current segment ACDEG . 1. hatwide F = ˆ 2. hatwide F = 1 2 ˆ ı ) 3. hatwide F = 1 2 ı ˆ ) 4. hatwide F = ˆ 5. hatwide F = ˆ ı 6. hatwide F = ˆ ı correct 7. Undetermined, since the magnitude of the force is zero. 8. hatwide F = 1 2 ı + ˆ ) 9. hatwide F = ˆ k 10. hatwide F = ˆ k Explanation: Note: The force on wire segment AC is canceled by the force on wire segment EG .
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