Explanation Given: 1) A current i at time t which is producing magnetic field B is defined by following formula i ( t ) = t ( 12 − t ) 2) Magnitude of produced magnetic field B is as follows B = μ 0 i 2 π r T Where μ 0 = 4 π × 10 − 7 T − m / A i = current passing through the wire r = distance of magnetic field from wire 3) The area through which the flux needs to be calculated is rectangle of dimension L × H = 3 × 2 m , and top and bottom edges are parallel to wire. Bottom edge of rectangle is located at d = 0.5 m above the wire. 4) Given figure is follows Formula used: 1) Flux of magnetic field is given by ϕ = ∬ S F . d S 2) ∫ 1 x d x = log x 3) ∫ x n d x = x n + 1 n + 1 4) Faraday’s law states that voltage drop around the closed surface can be determine by differentiation of flux with respect to time is Voltage drop = d ϕ d t Calculation: Flux ϕ ( t ) = ∬ S B . d S [using formula ϕ = ∬ S F . d S ] B = μ 0 i 2 π r [given] Area through which the flux needs to be calculated is rectangle of dimension L × H = 3 × 2 m Assuming the wire is on x -axis following diagram is simplified version of given figure to get the properties of flux area ABCD is flux area. So to calculate flux we need to perform double integration that is surface integration and equation can be rewrite as ϕ ( t ) = ∫ 0 3 ∫ 0.5 2.5 B . d S Putting value of B we get ϕ ( t ) = ∫ 0 3 ∫ 0...

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ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 17.5, Problem 32E

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The flux of magnetic field through particulars area, produced by current flowing through a straight wire and voltage drop around the rectangular loop using Faraday’s law.

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Chapter 17.5, Problem 31E

Chapter 17.5, Problem 33E

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Chapter 17 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

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The flux of magnetic field through particulars area, produced by current flowing through a straight wire and voltage drop around the rectangular loop using Faraday’s law.

Solution Summary: The author calculates the flux of magnetic field through particulars area, produced by current flowing through a straight wire and voltage drop around the rectangular loop using Faraday's law.

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To Calculate: The flux of magnetic field through particulars area, produced by current flowing through a straight wire and voltage drop around the rectangular loop using Faraday’s law.

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Chapter 17 Solutions

To Calculate:

The flux of magnetic field through particulars area, produced by current flowing through a straight wire and voltage drop around the rectangular loop using Faraday’s law.