Consider the rectangular (an amperian loop) path of length L and width w shown in Figure 5.2 (right).We can apply Ampère's law to this path by evaluating the integral of E-de over each side of the rectangle.The contribution along side 3 is zero because the magnetic field is zero outside the solenoid. Thecontributions from sides 2 and 4 are both zero, because is perpendicular to då along these paths, bothinside and outside the solenoid Side 1 gives a contribution to the integral because along this path 5 isuniform and parallel to dž, that is, the only contribution comes from path 1.BldsBidsBldsB=0fE dš = B đš + B-dš + B đš + B-d3 = BL = 4olencipath 1path 2path 3path 4If N is the mumber of tums in the length L, the total curent through the rectangle is NI. Therefore,Ampère's law applied to this path givesNB-ds = BL = H9NI =B = H0 = Honl5.2where n = N/L is the number of tums per unit length.Consider a section of the solenoid of length dx'. The total current winding around the solenoid in thatsection is dI = nidx'. This section is located at a distance x – x' away from the point P. The contributionto the magnetic field at P due to this subset of loops isHOR?2[(x – x')² + R²]ª/2HOR?dB =dl =-5.32[(x - x')? + R2j3/2 nldxIntegrating over the entire length of the solenoid, we obtain+L/2|+L/2dx'HonIR?(x – x')[(x – x')² + R°j³/2R²[(x – x')² + R*Il_1/2Honix+L/2x- L/25.42 l(x +L/2)2 +R2V(x- L/2)² + R²Equation 5.4 expresses the change of magnetic field depending on the distance from the center. 2. Calculate the expected ratio of the magnetic field between the ends of the solenoid(x = L/2 or – L/2) and its center (x = 0) for a finite length solenoid for L~R and L » R cases byusing Equation 5.4.

Answered: Image /qna-images/answer/08802c88-b493-466c-ab97-b7d210d3995f.jpg

2. Calculate the expected ratio of the magnetic field between the ends of the solenoid (x = L/2 or – L/2) and its center (x = 0) for a finite length solenoid for L~R and L » R cases by using Equation 5.4.

2. Calculate the expected ratio of the magnetic field between the ends of the solenoid (x = L/2 or – L/2) and its center (x = 0) for a finite length solenoid for L~R and L » R cases by using Equation 5.4.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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