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Homework 16 Solutions

# Homework 16 Solutions - lim(kl9356 Homework 16...

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lim (kl9356) – Homework 16 – Weathers – (22202) 1 This print-out should have 14 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points The plane of a rectangular coil of dimension 5 cm by 8 cm is perpendicular to the direction of a magnetic field B . The coil has 171 turns and a total resistance of 10 . 3 Ω. At what rate must the magnitude of B change in order to induce a current of 0 . 0368 A in the windings of the coil? Correct answer: 0 . 554152 T / s. Explanation: Basic Concepts: Faraday’s Law of Induc- tion E = d Φ B dt Ohm’s law I = V R Solution: With Ohm’s law, the emf induced in one turn of coil is E 1 = I R n = (0 . 0368 A) (10 . 3 Ω) (171 turns) = 0 . 00221661 V , while with Faraday’s law, we get E 1 = d Φ B dt = d ( A · B ) dt = A d B dt . So, the rate at which magnetic field changes will be d B dt = E 1 A = (0 . 00221661 V) (0 . 004 m 2 ) = 0 . 554152 T / s . 002 (part 1 of 2) 10.0 points The counter-clockwise circulating current in a solenoid is increasing at a rate of 9 . 44 A / s. The cross-sectional area of the solenoid is 3 . 14159 cm 2 , and there are 330 turns on its 12 . 2 cm length. What is the magnitude of the induced E produced by the increasing current? Correct answer: 3 . 32659 mV. Explanation: Faraday’s Law for solenoid: E = N d Φ dt = N A d B dt . Magnetic field produced by the changing current is B = μ 0 N I L d B d t = μ 0 N L d I d t . Faraday’s Law for solenoid: E = N d Φ dt = N d ( BA ) dt = N 2 A L μ 0 d I d t . Magnetic field induced by current: B = μ 0 N I L . Thus, the induced E is |E| = μ 0 N 2 L A d I dt = (1 . 25664 × 10 - 6 N / A 2 ) (330) 2 12 . 2 cm × (3 . 14159 cm 2 ) (9 . 44 A / s) × parenleftbigg 10 3 mV V parenrightbigg parenleftbigg 1 10 - 2 m cm parenrightbigg = 3 . 32659 mV .

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lim (kl9356) – Homework 16 – Weathers – (22202) 2 003 (part 2 of 2) 10.0 points Choose the correct statement 1. The E attempts to move the current in the solenoid in the clockwise direction correct 2. Not enough information is given to deter- mine the effect of the E 3. The E does not effect the current in the solenoid 4. By the right hand rule, the E produces magnetic fields in a direction perpendicular to the prevailing magnetic field 5. The E tries to keep the current in the solenoid flowing in the counter-clockwise di- rection Explanation: As the current is increasing in the counter- clockwise direction, by Lenz’s law, the E will attempt to retard the current, which estab- lishes an E that tries to counter the flow of the current, which in this case would be in the clockwise direction. 004 10.0 points An 18 . 6 turns circular coil with radius 9 . 56 cm and resistance 6 . 87 Ω is placed in a magnetic field directed perpendicular to the plane of the coil. The magnitude of the magnetic field varies in time according to the expression B = a 1 t + a 2 t 2 , where a 1 = 0 . 0934 T / s, a 2 = 0 . 0962 T / s 2 are constants, time t is in seconds and field B is in Tesla.
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Homework 16 Solutions - lim(kl9356 Homework 16...

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