Explanation Given: 1) A current i at time t which is producing magnetic field B is defined by following formula i ( t ) = 10 e − 0.1 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 the isosceles triangle of base 12cm and height 6cm, whose bottom edge is 3cm from the wire. 4) Given figure is follows Formula used: 1) Flux of magnetic field is given by ϕ = ∬ S F . d S 2) 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 3) If A = ( x 1 , y 1 ) and B = ( x 2 , y 2 ) then equation of line A B is x − x 1 x 2 − x 1 = y − y 1 y 2 − y 1 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 isosceles triangle having base 12cm and height is 6cm. Assuming the wire is on x -axis following diagram is simplified version of fig 17 to get the characteristics of flux area Calculating equation of line OB and BA which will be use in further calculation, Equation of line OB is x − 0 6 − 0 = y − 3 9 − 3 [using formula x − x 1 x 2 − x 1 = y − y 1 y 2 − y 1 ] x 6 = y − 3 6 x + 3 = y Equation of line BA is x − 6 12 − 6 = y − 9 3 − 9 [using formula x − x 1 x 2 − x 1 = y − y 1 y 2 − y 1 ] x − 6 6 = y − 9 − 6 x + y = 15 Consider a strip on a triangle OAB, which is parallel to x -axis ϕ ( t ) = ∬ S B ...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

See similar textbooks

Videos

Question

Chapter 17.5, Problem 33E

To determine

To Calculate:

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

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 17.5, Problem 32E

Chapter 17.5, Problem 34E

Students have asked these similar questions

(10 points) Let f(x, y, z) = ze²²+y². Let E = {(x, y, z) | x² + y² ≤ 4,2 ≤ z ≤ 3}. Calculate the integral f(x, y, z) dv. E

(12 points) Let E={(x, y, z)|x²+ y² + z² ≤ 4, x, y, z > 0}. (a) (4 points) Describe the region E using spherical coordinates, that is, find p, 0, and such that (x, y, z) (psin cos 0, psin sin 0, p cos) € E. (b) (8 points) Calculate the integral E xyz dV using spherical coordinates.

(10 points) Let f(x, y, z) = ze²²+y². Let E = {(x, y, z) | x² + y² ≤ 4,2 ≤ z < 3}. Calculate the integral y, f(x, y, z) dV.

Chapter 17 Solutions

Calculus - Standalone book

Ch. 17.1 - Prob. 1PQ Ch. 17.1 - Prob. 2PQ Ch. 17.1 - Prob. 3PQ Ch. 17.1 - Prob. 4PQ Ch. 17.1 - Prob. 1E Ch. 17.1 - Prob. 2E Ch. 17.1 - Prob. 3E Ch. 17.1 - Prob. 4E Ch. 17.1 - Prob. 5E Ch. 17.1 - Prob. 6E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

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

Videos

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

Want to see the full answer?

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 triangular loop using Faraday’s law.