1165 Chapter 301. The flux ΦBBA=cosθdoes not change as the loop is rotated. Faraday’s law only leads to a nonzero induced emf when the flux is changing, so the result in this instance is zero. 2. Using Faraday’s law, the induced emf is ()()()()()2220.12m0.800T0.750m/s0.452V.Bdrd BAddAdrBBrBdtdtdtdtdtπεππΦ= −= −= −= −= −= −−=3. The total induced emf is given by ()20002()()1.5 A(120)(4T m A)(22000/m)0.016m0.025 s0.16V.BddBddidiNNANAniNnANnrdtdtdtdtdtεμμμπΦ⎛⎞= −= −= −= −= −⎜⎟⎝⎠⎛⎞= −×⋅⎜⎟⎝⎠=-7p10pOhm’s law then yields ||/0.016 V /5.30.030 AiRε==Ω =. 4. (a) We use ε= –dΦB/dt = –πr2dB/dt. For 0 < t< 2.0 s: ()2220.5T0.12m1.1 10V.2.0sdBrdtε−⎛⎞= −= −= −×⎜⎟⎝⎠pp(b) For 2.0 s < t< 4.0 s: ε∝dB/dt= 0. (c) For 4.0 s < t< 6.0 s: ε= −= −−−FHGIKJ=×−pprdBdt222012056 04 01110......mTssVbg5. The field (due to the current in the straight wire) is out of the page in the upper half of the circle and is into the page in the lower half of the circle, producing zero net flux, at any time. There is no induced current in the circle.
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