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F05Exam1Solutions

# F05Exam1Solutions - PHYSICS 222 FALL 2005 EXAM#1 SOLUTIONS...

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1 PHYSICS 222, FALL 2005 EXAM #1 SOLUTIONS SEPTEMBER 29, 2005 Note: i ˆ , j ˆ , and k ˆ are unit vectors directed in the +x, +y, and +z directions, respectively, of a right-handed Cartesian coordinate system. Problems 1-15 are worth 2 points each. 1. At some instant of time, a negatively charged particle is moving with velocity v = v i ˆ in a magnetic field B = B k ˆ , where v is the particle's speed and B is the magnitude of B . The direction of the magnetic force on the particle is ____ . A. i ˆ B. i ˆ C. j ˆ D. j ˆ E. k ˆ Since the particle has a negative charge q, one has q = |q|. Thus, F = q v × B = |q|vB ( i ˆ × k ˆ ) = |q|vB ( j ˆ ) = |q|vB j ˆ . 2. A current-carrying circular coil with a magnetic moment µ is in a uniform magnetic field B . The maximum magnitude of the magnetic torque on the coil occurs when the angle between µ and B is ____ degrees. A. 0 B. 45 C. 90 D. 135 E. 180 τ = µ B sin φ , so the maximum torque occurs when sin φ = 1, giving φ = 90˚ . 3. A sphere of radius R is in a uniform magnetic field of magnitude B. The magnitude of the net magnetic flux through the surface of the sphere is ____ . A. 0 B. π R 2 B C. 2 π R 2 B D. 4 π R 2 B E. 8 π R 2 B For a closed surface, Gauss' law for magnetism is Φ B = O B · d A = 0 . 4. Two long thin straight parallel wires each carry the same magnitude of current I but in opposite directions. The distance between the axes of the wires is d. The magnitude of the (net) magnetic field at a point midway between the two axes of the wires is ____. Using the circular right-hand rule, one finds that each wire produces a magnetic field at P that is in the same direction. Since the distance from P to the axis of each wire (= d/2) is the same, the magnitude of the field contribution from each wire is the same: B = µ o I/( π d). The sum of these two magnitudes is twice the value for each one: B = 2 µ o I/( π d) . 5. The magnetic field at the center of a circular wire loop of radius R and carrying a current I ____

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F05Exam1Solutions - PHYSICS 222 FALL 2005 EXAM#1 SOLUTIONS...

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