Explanation Write the expression for the induced emf in the loop. e = − d Φ B d t (I) Here, e is induced emf, Φ B is magnetic flux and d t is change in time. Write the expression for magnetic flux in small rectangular region of width d r and length l . Φ B = ∫ ( B l ) d r (II) Here, B is magnetic field due to wire. Write the expression for magnetic field at distance r , from the wire. B = μ 0 I 2 π r Here, μ 0 is magnetic permeability of space, I is current flowing in wire. Write the expression for induced current in the loop. I = e R (III) Here, I is current and R is resistance of the loop. Substitute μ 0 I 2 π r for B in equation (II) to find the flux. Φ B = l ∫ ( μ 0 I 2 π r ) d r Integrating above expression with respect to r between r to r + w to find total flux. Φ B = l ∫ r r + w ( μ 0 I 2 π r ) d r = μ 0 I l 2 π [ ln r ] r r + w = μ 0 I l 2 π ln r + w r = μ 0 I l 2 π ln ( 1 + w r ) Here, w is width of rectangular loop

Physics for Scientists and Engineers With Modern Physics

9th Edition

ISBN: 9781133953982

Author: SERWAY, Raymond A./

Publisher: Cengage Learning

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Chapter 31, Problem 76AP

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Physics for Scientists and Engineers With Modern Physics

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