Correct answer 1 n explanation lorentzs force f q v b

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Correct answer: 1 . 00624 × 10 - 20 N. Explanation: Lorentz’s Force ~ F = q ( ~v × ~ B + ~ E ) . Faraday’s Law in general form E = I ~ E · d~s = d Φ B dt .
Platt, David – Homework 22 – Due: Oct 31 2005, 4:00 am – Inst: Ken Shih 4 Lorentz’s Force ~ F = q ( ~v × ~ B + ~ E ) . at P , there is only induced electric field and no magnetic field, so Lorentz’s equation can be simplified as ~ F = q ~ E . To calculate electric field at P , note that the magnetic field region is circular, so there is a symmetry for the induced electric field, i.e. , they are equal magnitudely for all points on a circle of radius r away from the center of the magnetic field; so I ~ E d~s = 2 π r E , while d Φ B dt = d ( B · A ) dt = d ( B · π R 2 ) dt = π R 2 d B dt = π R 2 (3 d t 2 - 2 a t ) . From Faraday’s Law in general form, we get 2 π r E = πR 2 ( 3 d t 2 - 2 a t ) ; i.e. , E = R 2 2 r ( 3 d t 2 - 2 a t ) = (0 . 018 m) 2 2 (0 . 0474 m) h 3 (2 T / s 3 ) (2 . 49 s) 2 - 2 (3 . 78 T / s 2 ) (2 . 49 s) i = 0 . 0628047 N / C , and so the magnitude of the force exerted on the electron is F = q e E = (1 . 60218 × 10 - 19 C) (0 . 0628047 N / C) = 1 . 00624 × 10 - 20 N k ~ F k = 1 . 00624 × 10 - 20 N . 007 (part 2 of 3) 10 points And direction of the force is 1. same as that of the magnetic field. 2. opposite to that of the electric field. cor- rect 3. opposite to that of the magnetic field. 4. same as that of the electric field. 5. not determinable due to insufficient infor- mation. 6. perpendicular to that of the electric field and magnetic field. Explanation: The direction of the force is opposite to that of the electric field ~ E , since the charge on the electron is negative. 008 (part 3 of 3) 10 points At what (non-zero) time is this force equal to zero? Correct answer: 1 . 26 s. Explanation: The F = 0 if and only if the electric field is zero. From explanation for Part 1 we know E = R 2 2 r d B dt from this we get the condition for the F = 0 is d B dt = 0 i.e. , 3 d t 2 - 2 a t = 0 So, t = 0 s or t = 2 a 3 d = 2 (3 . 78 T / s 2 ) 3 (2 T / s 3 ) = 1 . 26 s . The t = 0 solution is trivial!
Platt, David – Homework 23 – Due: Nov 2 2005, 4:00 am – Inst: Ken Shih 1 This print-out should have 7 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points A circuit consists of a 32 Ω resistor and a 740 mH inductor connected in series to a 17 V battery. What is the value of the current when the current is increasing at the rate of 4 A / s? Correct answer: 0 . 43875 A. Explanation: Let : R = 32 Ω , L = 740 mH = 0 . 74 H , V = 17 V , and Δ i Δ i = 4 A / s . In an RL circuit V = L Δ i Δ t + i R i = V - L Δ i Δ t R i = 17 V - (740 mH) (4 A / s) 32 Ω i = 0 . 43875 A 002 (part 1 of 1) 10 points In the circuit below a steady current I 0 is flowing when the switch is in position “a”. If the switch is then thrown to position “b”, the current will decrease to zero after some time. L R E S b a I ( t ) Suppose we replace the inductor with one of the same area and length, but twice as many turns.

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