CHAPTER: 4 MOVING CHARGES AND MAGNETISM

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CHAPTER: 4 MOVING CHARGES AND MAGNETISM 1 Define electic Loentz foce * It is the foce expeienced by a chaged paticle at est o oving in an electic field F E E 2 Define Magnetic Loentz foce * It is the

1 CHAPTER: 4 MOVING CHARGES AND MAGNETISM 1 Define electic Loentz foce * It is the foce expeienced by a chaged paticle at est o oving in an electic field F E E 2 Define Magnetic Loentz foce * It is the foce acting on a chaged paticle oving in a agnetic field F B ( v X B ) vb Sinθ Whee v velocity of the paticle B Magnetic field θ angle between v and B [Foce acts in a diection pependicula to both the velocity and the agnetic field given by ight hand scew ule] 3 Can a chaged paticle ove in a agnetic field, without expeiencing any foce? *Yes it can But only when it oves paallel o anti paallel to the field When it oves paallel to the field, When θ 0, F B vb Sin0 0 o When θ 180, F B vb Sin Define Loentz Foce * It is the total foce acting on a chaged paticle oving in the cobined effect of electic and agnetic fields F F E + F B ( E + v X B ) 4 What ae the units of agnetic induction (agnetic flux density)? *SI unit is tesla (T) Tesla is a athe lage unit A salle unit called gauss is also used 1 gauss 10-4 tesla 5 Define 1 tesla * We have F B v B Sinθ If, 1C, θ90 0 v 1/s and F 1N, then B 1 tesla B is 1 tesla, When the foce acting on a unit chage (1 C), oving pependicula to B with a speed 1/s, is one newton 6 Deive an expession fo the agnetic foce acting on a cuent caying conducto placed in a unifo agnetic field Conside a conducto of aea of coss section A and length placed in a unifo agnetic field Let n be the no of fee electons pe unit volue of the conducto Total nube of electons in the conducto Volue n A n Total chage, A ne Foce on the conducto, F B ( v d X B ) Whee v d dift velocity F B A ne ( v d X B ) F B ne A v d ( X B ) F B I ( X B ) I neavd The diection of this foce is given by Fleing s left hand ule 7 State Fleing s left hand ule * Stetch the thee finges in you left hand in thee utually pependicula diections If the foefinge gives the diection of agnetic field and the iddle finge gives the diection of cuent, then the thub will give the diection of foce on the conducto Cycloton 8 What is the use of a cycloton? Explain its constuction and woking Wite its pinciple 1 P a g e

2 Deive expessions fo axiu kinetic enegy and cycloton feuency Use: - Cycloton is a paticle acceleato used to acceleate chaged paticles to vey high enegy Constuction:- Cycloton consist of (i) two seicicula D-shaped chabes called Dees (ii) an RF oscillato to supply AC voltage (electic field) of paticula feuency (iii) an ion souce at the cente to poduce ions (iv) a deflecto and (v) a pependicula agnetic field The whole aangeent is placed in an evacuated chabe to iniize collisions between ions and ai olecules Woking:- Conside at any instant a positive ion poduced at the cente Let at that tie D1 is positive and D2 is negative The positive ion entes D2, copletes a sei-cicula path and eaches the gap When the paticle eaches the gap, the polaities of the Dees ae evesed and D1 becoes negative The positive ion entes D1 and it copletes a cicula path This pocess epeats Inside the Dees the paticles tavel in a egion fee of electic field due to electostatic shielding Since the velocity of the ion inceases the adius of the cicula path also inceases Finally, when the adius of the cicula path becoes nealy eual to the adius of the Dee, the ion is deflected by the deflecto and it hits the taget Pinciple:- The feuency of evolution of the chaged paticle in a agnetic field is independent of its enegy In a pependicula agnetic field, a chaged paticle oves in a cicula path The necessay centipetal foce fo the evolution of the paticle is povided by the agnetic foce, F v2 vb The chaged paticle gets acceleated by the electic field Expession fo KE:- Centipetal foce Magnetic Loentz foce v 2 v B v B v B Fo e(3), it is clea that α v ie, when velocity inceases, adius of the cicula path also inceases KE of the paticle, KE ½ v 2 ½ ( B KE ½ 2 B 2 2 KE is axiu when appoaches R, the adius of the dees (R) KE ax ½ 2 B 2 R 2 Cycloton Feuency (υc):- The angula feuency of the chaged paticle, ω v B ) 2 2 P a g e

3 Theefoe, the tie peiod of evolution of the paticle, T 2 π 2 π ω B Fo esonance the tie peiod of the RF oscillato ust be sae as the tie peiod of evolution of the paticle So the tie peiod of the RF oscillato should be T 2 π B Feuency of the cycloton, υ 1 T B 2 π υc B 2 π This feuency is called cycloton feuency o esonance feuency Applications:- 1 Cycloton is used to bobad nuclei with enegetic paticles, so acceleated by it, and study the esulting nuclea eactions 2 It is used in hospitals to poduce adioactive substances which can be used in diagnosis and teatent 9 What ae the liitations of cycloton? 1 Cycloton cannot be used to acceleate unchaged paticles 2 Only suitable fo acceleating heavie paticles 3 Cycloton cannot acceleate chaged paticles to a speed nea to the speed of light (elativistic speed) If a +ve ion is acceleated to the speed of light, its ass vaies accoding 0 to theoy of elativity as, 1- v2 c 2 Theefoe the feuency of evolution will not be a constant So the ion cannot be acceleated beyond a cetain liit 4 Electon cannot be acceleated using a cycloton Reason: - Since electon has vey low ass, its velocity inceases to a vey high value even on the application of a sall EF Theefoe, electon cannot be in phase with the RF Oscillato Biot Savat Law 10 State Biot Savat Law Biot-Savat law states that the agnetic field at a point due to the sall eleent of a cuent caying conducto is diectly popotional to 1 The cuent (I) flowing though the conducto 2 The length (dl) of the eleent 3 Sine of the angle (θ) between and dl and invesely popotional to the suae of the distance ( 2 ) of the point fo dl db α Idl Sin θ 2 db μ 0 In vecto fo, db μ 0 db μ 0 db μ 0 Idl x 2 Idl x 3 Idl x 2 x Idl Sin θ 2 μ0 is called the peeability of fee space (o vacuu) μ0 4π 10-7 T/A The diection of this field is given by ight hand scew ule (db is pependicula to dl & ) By ight hand scew ule, otate a ight hand scee fo I dl to, the tip of the scew advances gives diection of db 3 P a g e

4 11 Deive the elation between ε0 and μ0 μ0ε0 4π ε0 [ μ 0 ] 1 9x 10 9 x x (3x 10 8 ) 2 1 c 2 C-Speed of light in vacuu 12 Using Biot-Savat law, find the agnetic field on the axis of a cicula cuent loop (cicula coil) But, dl 2πR μ 0 I R B (x 2 + R 2 ) 3/2 2πR μ 0 I R 2 B 2(x 2 + R 2 ) 3/2 Fo a coil of N tuns, μ 0 N I R 2 B 2(x 2 + R 2 ) 3/2 Magnetic field at the cente of the cicula coil is obtained by putting x0, B μ 0 N I R 2 2( R 2 ) 3/2 μ 0 N I 2R The diection of this ag field is given by the ight-hand thub ule Magnetic field at P due to the sall eleent dl at A, db μ 0 Idl Sin db μ 0 Idl 2 μ 0 Idl x 2 + R 2 db can be split into two coponents dbcosθ along PY and dbsinθ along PX If we conside anothe eleent B of the loop at diaetically opposite end B, dbcosθ coponents cancel each othe Thus thee is agnetic field only along PX So the total agnetic field at P, B db Sinθ μ 0 Idl x 2 +R 2 Sinθ But Sinθ R R (x 2 + R 2 ) ½ Substituting, B μ 0 μ 0 B Idl x 2 +R 2 R (x 2 + R 2 ) ½ I R (x 2 + R 2 ) 3/2 dl 13 State Apee s cicuital law *Apee s cicuital law states that the line integal of agnetic field ove a closed path is eual to μ0 ties the total cuent enclosed by the path B dl μ0 I 14 What ae the applications of Apee s law? * Apees law can be applied to find the agnetic field due to: (i) a staight infinitely long conducting wie (ii) a solenoid & (iii) a tooid 15 Applying Apees law, deive an expession fo the agnetic field due to a staight infinite cuent caying wie 4 P a g e

5 * To find the f due to the staight cuent caying conducto at a point P, distant R fo the conducto, iagine an apeian loop of adius R 18 Deive expessions Application Magnetic field due to a long solenoid Ove the apeian loop both B & dl ae along the sae diectiontheefoe θ 0, B dl B dl Cos θ μ0 I l B dl Cos 0 μ0 I l B dl μ0 I [Since B is l constant ove the apeian loop] B 2πR μ0 I B μ0 I 2πR 17What is a solenoid? *Solenoid is a long insulated wie wound in the fo of a helix whee the neighbouing tuns ae closely spaced When cuent flows though the solenoid, it behaves as a ba agnet Fo a long solenoid, the field outside is nealy zeo The field inside is eveywhee paallel to the axis If the cuent at one end of the solenoid is in the anticlockwise diection it will be the Noth Pole and if the cuent is in the clockwise diection it will be the South Pole Accoding to Apee s law B dl μ0 NI, whee N- is the nube of tuns of the solenoid inside the loop B dl B dl + B dl + s p s B dl + B dl μ0 NI B dl 0, the side s is outside the solenoid whee B0 B dl Cos 0+ B dl Cos 90+ p B dl Cos 90 μ0 NI s B dl B dl Cos μ0 NI p s B x l μ0 NI μ0 NI B l μ0 n I (coe is ai) Whee n N l is noof tuns pe unit length *If the coe is a ateial of elative peeability μ then, B μ0 μ n I Note: At the end points of the solenoid, μ0 ni B 2 19 How can you incease the agnetic field of a solenoid? * The agnetic field due to a solenoid can be inceased by i) Inceasing the no of tuns pe unit length (n) ii) Inceasing the cuent (I) iii) Inseting a soft ion coe into the solenoid 20 What is a tooid? 5 P a g e

6 * It is a long solenoid bent into the fo of a cicle 21 Applying Apee s law deive an expession fo the agnetic field due to a tooid 22 Deive an expession fo the foce between two paallel staight cuent caying conductos *Conside two staight paallel conductos of lengths l 1, l 2 and caying cuents I1 and I2 placed at a sepaation d Case 1- Field point inside the tooid:- Applying Apee s law ove the closed loop C1, B dl μ0 I enclosed C1 But I endosed by the apeian loop is zeo B0 Case 2- Field at point P on the cicula axis of the tooid:- Applying Apee s law ove the closed loop C2, B dl μ0 N I enclosed C2 B dl Cos 0 μ0 N I enclosed C2 B x 2π 2 μ0 N I enclosed N B But 2π n 2 μ0 NI 2π 2 B μ0 n I Case3- Field point P is outside tooid:- Applying Apee s law ove the closed loop C3, B dl μ0 I enclosed C3 But I endosed by the apeian loop is zeo [Since cuent enteing the plane of the pape is cancelled by the cuent leaving fo the plane of the pape] B0 Thee is no agnetic field outside the tooid Magnetic field at a distance d due to the fist cuent caying conducto P is, B1 μ0 I1 2πd The second conducto (Q) is placed in the agnetic field of the fist conducto Then the foce on it is, F I2 ( 2 X B1 ) F I ( X B ) F I2 2 B1 Sin 90 I2 2 B1 μ0 I1 μ0 I1 I2 2 2πd I2 2 2πd Foce pe unit length of the conducto is, f F μ0 I1 I2 2 2πd Natue (o type) of foce *If the cuents ae in the sae diection, the foce is attactive *If the cuents ae in the opposite diections, the foce is epulsive 23 Define 1 Apee * The foce pe unit length between two cuent caying staight conductos, f F μ0 I1 I2 2 2πd Put I1 I2 1A and d 1 then, μ0 x1x1 f μ0 4π x10-7 2π x1 2π 2π 2x10-7 N/ 6 P a g e

*One apee is the value of that steady cuent which, when aintained in two staight paallel conductos of infinite length and of negligible coss section, placed 1 apat in vacuu, would poduce a foce of 2

7 *One apee is the value of that steady cuent which, when aintained in two staight paallel conductos of infinite length and of negligible coss section, placed 1 apat in vacuu, would poduce a foce of N/ on each conducto 24 Define agnetic dipole oent due to a cuent * Magnetic oent, Cuent Aea IA Fo a coil having n tuns N tuns NIA, SI unit is A 2 25 Deive an expession fo the toue on a ectangula cuent loop in a agnetic field *Conside a ectangula loop of wie ps of sides l and b, caying cuent is placed in a unifo agnetic field B The as and ps expeience no foce as the cuent in the ae paallel to the diection of field B Foce on the side p (of length l) F B I l (diected inwads the plane of the pape) Foce on the side s, F B I l (diected outwads the plane of the pape) The foces on sides p and s ae eual and opposite but they ae not collinea So they constitute a toue Toue (τ) F x distance τ B I l x b B IA A l x b If the noal to the plane of the loop akes an angle θ with the diection of the field the, τ B IA Sin θ IABSin θ BSin θ τ x B I A 26 Deive an expession fo the agnetic oent of a evolving electon What is Boh agneton? An electon obiting aound a nucleus behaves like a cuent loop Cuent (I) t e T Whee T is the tie peiod of evolution of electon But T 2π V I e 2π V, whee v- obital speed e v 2π Magnetic oent(μ) IA μ e v 2π A e v 2π x π2 μ e v (μ l - is diected into the plane 2 of the pape) Angula oentu of the electon is, μ l L v v L el μ l 2 μ l e constant, called L 2 gyoagnetic atio e 2 88 x1010 C/kg L Boh agneton Accoding to Boh odel of H ato, L nh 2π, n is a natual nube, n 1, 2, 3, enh el μ l 2 2π enh 2 e 4π e eh Fo n1,( μ l )in 4π e 927 x10-24 A 2 This value is called Boh agneton 7 P a g e

8 Moving Coil Galvanoete 27 What is the use of a Moving coil Galvanoete (MCG)? * Moving coil galvanoete is used to detect the pesence of sall electic cuent and to give its diection With siple odifications, it can be used to easue cuent and voltage MCG consists of a ectangula coil of seveal tuns wound on a soft ion cylinde The cylinde is fee to otate between two concave shaped agnetic poles, which poduce adial agnetic field One end of the cylinde is attached to a sping, which poduces a estoing couple At the othe end a pointe is pivoted C θ NIAB θ ( NAB ) I C θ ( K ) I ie, deflection α cuent K NAB, is called C galvanoete constant 28 How can you convet a galvanoete into an aete? * Galvanoete can be conveted into aete by connecting a vey sall esistance (called shunt esistance) in paallel with it Pinciple When cuent flows though the coil, a toue acts on it In the adial agnetic field axiu toue is expeienced The toue, τ NIAB Sinθ The toue, τ NIAB (Sin90 1, θ90 fo adial field) Because of this toue, the coil otates, and then a estoing toue is developed in the sping Restoing toue, τ estoing Cθ whee C- is the couple pe unit twist (C estoing toue developed pe unit twist) and θ- is the angle of twist At euilibiu, We have, IgG (I Ig)S IgG S (I Ig) * Total Resistance of the G S aete is G + S Aete is a low esistance device So it is connected in seies with a cicuit, so that axiu cuent can pass though it, fo accuate easueent of cuent 29 Define cuent sensitivity of a galvanoete? θ I NAB, is called cuent C sensitivity Radian/apee 30 How can you incease the cuent sensitivity? θ NAB, I C i) Inceasing the aea of the coil (A) ii) Inceasing the f stength (B) iii) Inceasing the nube of tuns (N) 8 P a g e

9 iv) Deceasing the couple pe unit twist (C) 31 How can you convet a galvanoete into voltete? *Galvanoete can be conveted into voltete by connecting a lage esistance in seies with it 33 What is the use of soft ion coe in a MCG? * Soft ion coe has high peeability So it inceases the stength of the agnetic field Hence it inceases the sensitivity of the galvanoete We have, V Ig G + Ig R Ig R V Ig G R V - G Ig * Total Resistance of voltete is, G + R 33 Define voltage sensitivity of a galvanoete * θ I x 1 R NAB x 1 C R θ NAB, is called voltage V CR sensitivity adian/volt 32 How can you incease the voltage sensitivity of a galvanoete? Voltage sensitivity can be θ inceased by, NAB V CR i) Inceasing the aea of the coil (A) ii) Inceasing the stength of the f (B) iii) Deceasing the couple pe unit twist (C) Voltete is a high esistance device So it is connected paallel with a cicuit If we connect it in seies, then thee is no flow of cuent in the cicuit because of high esistance and no use of connecting it in seies because the potential diffeence between two points on the sae line is zeo 9 P a g e

FARADAY'S LAW. dates : No. of lectures allocated. Actual No. of lectures 3 9/5/09-14 /5/09

FARADAY'S LAW. dates : No. of lectures allocated. Actual No. of lectures 3 9/5/09-14 /5/09 FARADAY'S LAW No. of lectues allocated Actual No. of lectues dates : 3 9/5/09-14 /5/09 31.1 Faaday's Law of Induction In the pevious chapte we leaned that electic cuent poduces agnetic field. Afte this