Explanation 1) Concept: From the given F i g 29 - 68 , we can find the net current through the loop for paths 1 and 2 . Then by using Ampere’s law, we can find the value of integral ∮ B → . d s → for paths 1 and 2 . 2) Formula: According to Ampere’s law, ∮ B → . d s → = μ 0 i 3) Given: i) The current through loop 1 is i 1 = 5.0 A ii) The current through loop 2 is i 2 = 3.0 A 4) Calculations: According to Ampere’s law, ∮ B → . d s → = μ 0 i Where the integral is around a closed loop and i is the net current through the loop. a) For path 1 , using Ampere’s law, the integral is ∮ B → . d s → = μ 0 i But from F i g . 29 - 68 , the net current through the loop is i = - i 1 + i 2 Substituting the current in Ampere’s law, we get ∮ B → . d s → = μ 0 - i 1 + i 2 ∮ B → . d s → = ( 4 π × 10 - 7 T . m / A ) - 5.0 A + 3.0 A ∮ B → . d s → = ( 4 π × 10 - 7 T

10th Edition

ISBN: 9781118230725

Author: David Halliday, Robert Resnick, Jearl Walker

Publisher: Wiley, John & Sons, Incorporated

See similar textbooks

Question

Chapter 29, Problem 44P

To determine

To find:

The value of integral ∮B→.ds→ for

a) Path 1

b) Path 2

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 29, Problem 43P

Chapter 29, Problem 45P

Students have asked these similar questions

The figure shows two closed paths wrapped around two conducting loops carrying currents i₁ = 8.3 A and i₂= 3.5 A. What is the value of the integral $B ds for (a) path 1 and (b) path 2? (a) Number (b) Number Units Units

Problem 6: Two power lines, line 1 and line 2, both of length L 88 m, are strung east-west between two towers. line 1 is r12 1.1 m directly above line 2. The current in both power lines is IL- 77 A to the west. Assume the power lines are straight and you can use the approximation ri2 << L Randomized Variables LL 88 m 12 1.1 m IL-77 A A Part (a) Find the magnitude of the magnetic field B21, in teslas, produced by line 1 at Part (b) What is the direction of the magnetic field produced by line 1 at line 2? Part (c) Calculate the magnitude of the magnetic force F21, in newtons, that the line 2 South. Correct! current in line 1 exerts on line 2. Part (d) Assume a typical power line has a mass of 890 kg per 1000 m. How many times larger would the current in both lines have to be for the magnetic force on the line to balance the force of gravity? tan() acos() sinh0) sin cos(0) cotanO asin acos 4 5 6 atan()acotan(0 coshO cotanhO 0 Degrees O Radians BACKSPACE CLEAR Submit Hint I give up!

Figure 29-33 shows four identical currents i and five Amperian paths (a through e) encircling them. Rank the paths according to the value of f B ds taken in the directions shown, most positive first.