A moving charged particle creates a magnetic field vector at every point in space except at its position.

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Maurice Cole
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1 1 Pat 3: Magnetic Foce 3.1: Magnetic Foce & Field A. Chaged Paticles A moving chaged paticle ceates a magnetic field vecto at evey point in space ecept at its position. Symbol fo Magnetic Field mks units [Tesla = T = N/(A m)] othe common unit [Gauss = G] [1 G = 10-4 T] This magnetic field eets a magnetic foce on anothe moving chaged paticle. F = q v sin θ Diection: Foce Right Hand Rule #1 (Foce RHR #1) q q = chage of paticle v v = speed of paticle = angle between magnetic field & velocity vectos 1. Cul finges fom v diection into diection. 2. Thumb gives foce diection fo + chage. Foce diection is opposite fo chage. The size and diection of the magnetic foce can be epessed with one vecto equation using the coss poduct. F = qv

2 2. Motion of Chaged Paticles in -Fields f a chaged paticle moves though a unifom magnetic field, the path of the paticle will be: staight (no foce) if the angle between the velocity and field is 0 o 180 a cicula ac if the angle between the velocity and field is 90 a spial if the angle between the velocity and field is some othe angle Cicula Ac Motion Fo the cicula ac, whee the velocity is pependicula to the field, the foce is a centipetal foce which gives the paticle a centipetal acceleation. F = q v = mv2 m = mass of paticle = adius of cicle This foce equation can be solved fo the elevant quantity Application 1: Synchoton (Paticle Acceleato) Acceleate chage paticles with an electic foce as they tavel a cicula path with a fied adius. The magnetic field necessay to keep them moving in that cicle is found fom the above foce equation. = mv q

3 3 Application 2: Mass Spectomete onize atoms/molecules. Acceleate ions using an electic field. Send ions into a velocity selecto so that the ions that make it though the selecto have the same speed. Send these ions into a magnetic field so that they tavel cicula acs. Diffeent masses give diffeent ac adii so the masses of the ions can be distinguished. Thus, the ion species can be detemined. ions v E acceleating plates velocity selecto (pependicula E & fields) cicula ac egion ( field only) n the velocity selecto, the electic foce balances the magnetic foce only fo the ions that tavel at the taget speed of v = E nside the ac egion, the mass of the ion is found fom the above foce equation. m = q v C. Staight Wie A cuent-caying staight wie segment sitting in a magnetic field feels a magnetic foce. F = l sin θ = cuent = length of segment = angle between field & cuent diection Diection: Foce Right Hand Rule #2 (Foce RHR #2) 1. Cul finges fom diection into diection. 2. Thumb gives foce diection.

4 4 The size and diection of the magnetic foce can be epessed with one vecto equation using the coss poduct. F = l D. Cuent Loops & Motos f a cuent-caying coil of wie is sitting in a magnetic field, the net magnetic foce on the loop is zeo. Howeve, thee can be a net toque on the loop that can cause it to otate about a fied ais. Peak toque [N-m] τ ma = NA Aveage toque [N-m] τ ave = 2 π NA Mechanical powe (due to otation) [W = J/s] P = τω = 2πτf N = numbe of tuns in coil = magnetic field [T] A = aea of one tun [m 2 ] = cuent though coil [A] Eample: An electic moto has 200 windings whee each winding has an aea of 20 cm 2. The coil sits in a magnetic field of 0.01 T. A cuent of 5 A flows though the coil when it otates at 600 pm. Find (a) the aveage toque eeted on the coil and (b) the aveage powe it delives. Ans. (a) N-m (b) 8 W

5 5 3.2: Souces of Magnetic Field iot-savat Law A moving chage poduces a magnetic field at a point P given by diection of P = μ o 4π ds 2 ds + A. Staight Wie Field at a point due to the cuent in a staight wie segment = μ o 4πa (cos θ 1 cos θ 2 ) P a 1 2 Diection: Field Right Hand Rule #1 (Field RHR #1) 1. Place thumb along cuent so that finges touch point P. 2. Cul finges towads palm. The initial diection that the finges move is diection. Special Case: Long wie ( 1 0 and 2 180) = μ o 2πa

6 6. Two Paallel Wies f cuents flow though each wie segment, then these cuents poduce magnetic fields. These fields eet magnetic foces on the wies, equal and opposite in size. Size of foce: F = μ o 1 2 2πa 1 F 1 2 F 2 a C. Cuent Loop Field on the cental ais of a loop of adius R with a cuent μ o R 2 = 2( 2 + R 2 ) 3/2 R P Diection: Field Right Hand Rule #2 (Field RHR #2) 1. Follow aound loop with finges. 2. Thumb gives diection of along ais. Special Case: At loop s cente (=0) = μ o 2R

7 7 D. Solenoid (Coil) Field at a point on the cental ais of a solenoid with length and N tuns = μ on 2 (sin 1 sin 2 ) R N tuns 1 2 P Diection: Field Right Hand Rule #2 (Field RHR #2) 1. Follow aound coil with finges. 2. Thumb gives diection of along ais. Special Case: Long solenoid ( 1 90 and 2 90) = μ on E. Gauss Law fo Magnetism & Ampee s Law Gauss s Law fo Magnetism states that the magnetic flu though any closed suface is zeo. da = 0 This is a statement of the fact that magnetic field lines fom closed loops. Thee ae no magnetic monopoles obseved in natue. Ampee s Law is an altenative to the iot-savat Law fo finding the magnetic field due to a cuent. t is sometimes easie to use than the iot-savat Law. ds = μ o Like the iot-savat Law, Ampee s Law states that the magnetic field stength is popotional to the cuent.

Ch 30 - Sources of Magnetic Field! The Biot-Savart Law! = k m. r 2. Example 1! Example 2!

Ch 30 - Sources of Magnetic Field! The Biot-Savart Law! = k m. r 2. Example 1! Example 2! Ch 30 - Souces of Magnetic Field 1.) Example 1 Detemine the magnitude and diection of the magnetic field at the point O in the diagam. (Cuent flows fom top to bottom, adius of cuvatue.) Fo staight segments,