Right Hand Rule. Magnetic field is defined in terms of the force on a moving charge. B=F/qvsinΘ for a moving charge or F=qvxB.

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1 Magnetic field is defined in tems of the foce on a moving chage =/qvsinθ fo a moving chage o =qvx =/lsinθ o =lx fo a cuent Right Hand Rule Hold you ight hand open Place you finges in the diection of Place you thumb in the diection of v The diection of the foce on a positive chage is diected out of you palm f the chage is negative, the foce is opposite that detemined by the ight hand ule Question: The ight-hand ule fo the diection of the foce on a chaged paticle in a magnetic field applies: (a) only to positive chages (b) only to negative chages (c) to both positive and negative chages (d) only when the paticle is moving paallel to field. Answe: a Question: A chage paticle moves pependiculaly though a magnetic field. The effect of the field is to change the paticle s (a) chage (b) mass (c) velocity (d) enegy Answe: c Two chaged paticles of equal mass ae taveling in cicula obits in a egion of unifom, constant magnetic field as shown. The paticles ae obseved to move in cicula paths of adii R 1 and R 2 with speeds v 1 and v 2, espectively. As the figue shows, the path of paticle 2 has a smalle adius than that of paticle 1. Which one of the following statements about this system is false? (a) v 1 /Q 1 < v 2 /Q 2 X (b) Paticle 2 caies a positive chage. (c) Paticle 1 caies a negative chage. (d) Neithe paticle gains enegy fom the magnetic field. (e) The paticle velocities have no components paallel to the magnetic field. Magnetic ield of A Cuent oce between Cuents Solenoid

2 + ield aound long, staight cuent ~/ =μ o /2π (<<length of the wie) whee μ o =4πx10-7 T m/a is magnetic pemeability of fee space The diection of is detemined by the ight-hand ule Question: The magnetic field a distance d fom a long, staight wie is popotional to (a) d (b) d 2 (c) 1/d 2 (d) 1/d Answe: d Example: ind the magnetic field in ai 1 cm fom a wie that caies a cuent of 1 A. Solution: Since =10-2 m, we have =μ o /2π=(4πx10-7 T m/a)(1a)/2π10-2 m=2x10-5 T Question: Chaged paticles shown move in the vicinity of a cuent caying wie. o each chaged paticle, indicate the diection of magnetic foce due to the magnetic field geneated by the wie (Aow indicates the diection of motion of the paticle, + o indicates the sign of the chage. This is only a little smalle than the magnitude of the eath s magnetic field. o this eason geat cae is taken aboad ships to keep cuent-cay wies fom magnetic compasses A long, staight wie is caying a cuent of 5.0 A in the diection shown in the figue. The point P is m fom the wie. 1. What is the diection of the magnetic field at point P due to the cuent in the wie? (a) to the ight of page (d) into the plane of the page (b) to the left of the page (e) out of the plane of the pagex (c) towad the bottom of the page 2. What is the magnitude of the magnetic field at the point P? (a) 1.3x10 5 T (c) 2.5x10 5 T X (e) 9.4x10 5 T (b) 1.9x 10 5 T (d) 7.9x10 5 T +Q +Q L =μ o 1 /2π 2 =μ o 2 /2π The fields ae pependicula to the wie, i.e., sinθ=1, Θ=90 o L 12 = 2 L 1 = μ o 1 2 L/2π = 21 = 1 L 2 = μ o 1 2 L/2π /L= μ o 1 2 /2π

3 > Definition of Ampee: Definition of Ampee: f 1 = 2 =1A and =1 m then /L= N/m 1 C=1 A s (Q= t) QUCK QUZ 19.5 f 1 = 2 A and 2 = 6 A in the figue below, which of the following is tue: (a) 1 = 3 2, (b) 1 = 2, o (c) 1 = 2 /3? Ande Ampee: ench scientist ( ) QUCK QUZ 19.5 ANSWER (b). The two foces ae an actioneaction pai. They act on diffeent wies, and have equal magnitudes but opposite diections. Two long, staight, paallel wies sepaated by a distance d cay cuents in opposite diections as shown in the figue. The bottom wie caies a cuent of 6.0 A. Point C is at the midpoint between the wies and point O is a distance 0.50d below the 6-A wie as suggested in the figue. The total magnetic field at point O is zeo tesla. 1. Detemine the value of the cuent,, in the top wie. (a) 2 A (c) 6 A (e) This cannot be detemined since (b) 3 A (d) 18 A X the value of d is not specified. 2. Detemine the magnitude of the magnetic field at point C if d = 0.10 m. (a) 2.4x10 5 T (c) 9.6x10 5 T X (e) 1.4x10 4 T (b) 4.8x10 5 T (d) 1.1x10 4 T Magnetic field at the cente of a cuent loop =μ o /2π < =μ o /2 > Two loops cay equal cuents in the same diection. The loops ae held in the positions shown in the figue and ae then eleased. Which one of the following statements coectly descibes the subsequent behavio of the loops? (a) oth loops move to the left. (b) The loops emain in the positions shown. (c) The top loop moves to the ight; the bottom loop moves to the ight. (d) The loops epel each othe. (e) The loops attact each othe.x

4 Two long, staight wies ae pependicula to the plane of the pape as shown in the dawing. Each wie caies a cuent of magnitude. The cuents ae diected out of the pape towad you. Which one of the following expessions coectly gives the magnitude of the total magnetic field at the oigin of the x,y coodinate system? (a) μ o /2d (b) μ o /2πd (c) μ o / 2πd (d) μ o / 2d (e) μ o /d X The adius of a coil of wie with N tuns is = 0.22 m. A cuent coil = 2.0 A flows clockwise in the coil, as shown. A long, staight wie caying a cuent wie = 31 A towad the left is located 0.05 m fom the edge of the coil. The magnetic field at the cente of the coil is zeo tesla. Detemine N, the numbe of tuns. (a) 2 (b) 4 X (c) 3 (d) 1 (e) 6 Loops fo Real Magnets Magnetic field inside a solenoid =Nμ o /l=nμ o whee N is numbe of loops o tuns, l the length of the solenoid, and n the numbe of the loops pe unit length itte Disk loida-itte Disk =nμ o The lage, the stonge Example: A solenoid 20 cm long and 4 cm in diamete is wounded with a total of 200 tuns of wie. The solenoid is aligned with its axis paallel to the eath s magnetic field which is 3x10-5 T in magnitude. What should the cuent in the solenoid be in ode fo its field to exactly cancel the eath s field inside the solenoid? Solution: Since l=0.2 m and N=200 tuns, =Nμ o /l =l/μ o N=(3x10-5 T)(0.2)/(4πx10-7 Tm/A)(200)=0.024 A=24 ma The solenoid diamete has no significance except as a check that the solenoid is long elative to its diamete. =nμ o The lage n, the stonge

5 Question: When a feomagnetic substance is inseted in a cuent-caying solenoid, the magnetic field is (a) slightly deceased (b) geatly deceased (c) slightly inceased (d) geatly inceased Answe: d