( ) ( )( ) ˆ. Homework #8. Chapter 28

Transcription

1 Hoewok #8. Chapte 8 1** A sall cuent eleent at the oigin has a length of. and caies a cuent of. A in the +z diection. Find the agnitude of the agnetic field due to this eleent and indicate its diection on a diaga at (a)., y 4., z and (b)., y, z 4.. Pictue the Poble We can substitute fo and d l l in the iot-avat law ˆ dl ( d ), evaluate and ˆ fo the given points, and substitute to find d. Apply the iot-avat law to the dl ˆ d given cuent eleent to obtain: ( ) ( )( ) ˆ.A.k ˆ 1 N/A ˆ k ˆ (.4 nt ) (a) Find and ˆ fo the point whose coodinates ae (., 4., ): Evaluate d at (., 4., ): (. ) iˆ + ( 4. )j ˆ. 5, and ˆ iˆ + ˆj iˆ , ˆj d (.,4.,) (.4 nt ) 1 iˆ + 5 ( 5 ) 5 ˆ j ( 18pT) iˆ + ( 8.9pT)j ˆ

2 The diaga is shown to the ight: d y (., 4., ) (b) Find and ˆ fo the point whose coodinates ae (.,, 4. ): z (.) iˆ + ( 4.). 5, and ˆ iˆ + iˆ , Evaluate d d at (.,, 4. ): (.,,4.) (.4 nt ) 1.. iˆ (. 5 ) ( 8.9pT)j ˆ The diaga is shown to the ight: y z d (.,, 4. )

3 ** The cuent in the wie shown in figue below is 8. A. Find the agnetic field at point P. Note that the cuent segents a-b and e-f do not contibute to the agnetic field at point P. The cuent in the segents b-c, c-d, and d-e esult in a agnetic field at P that points into the plane of the pape. Note that the angles bpc and epd ae 45 and use the epession fo due to a staight wie segent to find the contibutions to the field at P of segents bc, cd, and de. c d a b Epess the esultant agnetic field at P: Epess the agnetic field due to a staight line segent: P e f + + bc cd de ( sinθ + sinθ ) 1 (1) Use equation (1) to epess de : Use equation (1) to epess bc and cd : bc cd ( sin 45 + sin ) sin 45 ( sin 45 + sin 45 ) sin 45 ubstitute to obtain: ubstitute nueical values and evaluate : sin 45 + sin 45 + sin 45 4 sin 45 8.A 4( 1 T /A) sin T into the page

4 3** An infinitely long wie lies along the ais, and caies cuent in the + diection. A second infinitely long wie lies along the y ais, and caies cuent in the +y diection. At what points in the z plane is the esultant agnetic field zeo? Let the nueal 1 denote the cuent flowing in the positive diection and the agnetic field esulting fo it and the nueal denote the cuent flowing in the positive y diection and the agnetic field esulting fo it. We can epess the agnetic field anywhee in the y plane using and the ight-hand ule and then ipose the condition that to deteine the set of points that satisfy this condition. Epess the esultant agnetic field 1 + (1) due to the two cuent-caying wies: Epess the agnetic field due to the cuent flowing in the positive diection: 1 1 y Epess the agnetic field due to the cuent flowing in the positive y diection: ubstitute fo 1and in equation (1) and siplify to obtain: y y because 1. Fo : y y. eveywhee on the plane that contains both the z ais and the line y in the z plane.

5 4** Find the agnetic oent of a thin ound loop with cuent if the adius of the loop is equal to 1 and the stength of the agnetic field at its cente is equal to 6. T.

6 5** Poble 8.37 fo you tetbook.

7 6** A tightly wound 1-tun tooid has an inne adius 1. c and an oute adius. c, and caies a cuent of 1.5 A. The tooid is centeed at the oigin with the centes of the individual tuns in the z plane. n the z plane: (a) What is the agnetic field stength at a distance of 1.1 c fo the oigin? (b) What is the agnetic field stength at a distance of 1.5 c fo the oigin? The agnetic field inside a tightly wound tooid is given by N ( π) whee a < < b and a and b ae the inne and oute adii of the tooid. Epess the agnetic field of a N tooid: π (a) ubstitute nueical values and evaluate (1.1 c):, ( ) ( 1 N/A )( 1)( 1.5A) 1.1 c π( 1.1 c) 7.3T (b) ubstitute nueical values and evaluate (1.5 c): ( ) ( 1 N/A )( 1)( 1.5A) 1.5 c π( 1.5 c). T

8 7** Nickel has a density of 8.7 g/c 3 and a ola ass of 58.7 g/ol. Nickel s satuation agnetization (agnetic field) is.61 T. Calculate the agnetic oent of a nickel ato in oh agnetons. We can find the agnetic oent of a nickel ato fo its elationship to the satuation agnetization using n whee n is the nube of olecules pe unit volue. n, in tun, can be found fo Avogado s nube, the density of N nickel, and its ola ass using A ρ n. Μ Epess the satuation agnetic field in tes of the nube of olecules pe unit volue and the agnetic oent of each olecule: n n Epess the nube of olecules pe unit volue in tes of Avogado s nube N A, the olecula ass, and the density ρ: ubstitute fo n in the equation fo and siplify to obtain: N A ρ n Μ NAρ Μ NAρ Μ N ρ A ubstitute nueical values and evaluate : 3 (.61T)( kg/ol) 3 3 ( 1 N/A )( 6. 1 atos/ol)( 8.7g/c ) A Divide by to obtain: A o.587 A A.587

9 8** A long thin solenoid has 5 tuns/c and caies a cuent of. A. The solenoid is filled with ion and the agnetic field is easued to be 1.7 T. (a) Neglecting end effects, what is the agnitude of the lied agnetic field? (b) What is the agnetization? (c) What is the elative peeability? Pictue the Poble We can use the equation descibing the agnetic field on the ais of a solenoid, as a function of the cuent in the solenoid, to find. We can then use + to find and K to evaluate K. (a) elate the agnetic field on the ais of a solenoid to the cuent in the solenoid: n ubstitute nueical values and evaluate : 1 ( 1 N/A )( 5c )(.A) 1.6 T (b) elate to and : + ubstitute nueical values and evaluate : 1.7T 1.6 T 7 1 N/A A/ (c) Epess in tes of K and : K K ubstitute nueical values and evaluate K : K 1.7T 1.6 T 137