Iportant Forulae & Basic concepts Unit 3: CHAPTER 4 - MAGNETIC EFFECTS OF CURRENT AND MAGNETISM CHAPTER 5 MAGNETISM AND MATTER S. No. Forula Description 1. Magnetic field induction at a point due to current eleent I current eleent (apere) dl sall eleent (eter) Idl sin θ db 4π r r distance fro the wire (eter) θ angle between r and dl (radians). Magnetic field induction at a point due to a linear conductor carrying current φ + φ 4πa B Isin( 1 ) 3. Magnetic field induction at a point due to a infinite long conductor B I 4πa 4. Magnetic field induction at the centre of circular coil πni B 4π r 5. Magnetic field induction at a point on the axis of the circular coil πnir B 4 π (r + x ) 3/ 7. Apere s circuital law B.dl I d I current (eter) a perpendicular distance (eter) φ 1 and φ angles (radians) a perpendicular distance (eter) r radius of the coil (eter) r radius of the coil (eter) x distance of the point fro the centre of the circular coil (eter) r radius of the coil (eter)
8. Magnetic field induction at a point inside the long solenoid B ni 9. Magnetic field induction at a point at one end on the axis of the long solenoid B ni 1. Magnetic field induction at a point inside the toroid B ni integral over closed loop. n no. of turns per unit length of solenoid (eter -1 ) n no. of turns per unit length of solenoid (eter -1 ) n no. of turns per unit length of solenoid (eter -1 ) 11. B at a point outside the toroid 1. Force on a charged particle inside electric field F qe 13. Force on a oving charged particle inside agnetic field F q(v B) 14. Radius of the circular path of a charged particle inside agnetic field r v qb F force (newton) E electric field (volt / eter) F force (newton) v velocity (eter / second) r radius (eter) v velocity (eter / second) ass of charged particle (kg) 15. Tie period of revolution r radius (eter)
T πr π v qb v velocity (eter / second) ass of charged particle (kg) 16. Cyclotron frequency 1 qb ν T π T tie period (second) ass of charged particle (kg) T tie period (second) 17. Maxiu kinetic energy of the charged particle B q r Eax ν frequency (hertz) ass of charged particle (kg) E ax Maxiu kinetic energy (joule) 18. Force on a current carrying conductor in agnetic field F I(l B) 19. Force per unit length on each of the two long parallel conductors carrying currents placed at a distance I1I F 4 π r. Torque on a current loop τ M B niabsin α M nia r radius (eter) F Force (newton) l length (eter) F Force per unit length on each of the two long parallel conductors (newton) I 1 current in one conductor (apere) I current in another conductor (apere) r separation between conductors (eter) M agnetic dipole oent of the loop (apere eter ) n nuber of turns in the coil A area of the coil (eter )
I current through the coil (apere) 3. Current through oving coil galvanoeter k I θ nba α angle which a noral drawn on the plane of coil akes with the direction of current θdeflection in galvanoeter (degrees) k restoring torque per unit twist (newton eter / degree) A area of each turn of the coil (eter ) n nuber of turns 4. Current sensitivity θ nba Is I k I s Current sensitivity (degree / apere) I current through galvanoeter (apere) θdeflection in galvanoeter (degrees) k restoring torque per unit twist (newton eter / degree) A area of each turn of the coil (eter ) n nuber of turns 5. Voltage sensitivity θ θ nba Vs V IR kr V s Voltage sensitivity (degree / volt) θdeflection in galvanoeter (degrees) V voltage across galvanoeter (volt) I current through galvanoeter (apere) R resistance of the coil (oh) k restoring torque per unit twist (newton eter / degree) A area of each turn of the coil (eter )
n nuber of turns 6. Full scale current in galvanoeter I nk g 7. Conversion of galvanoeter in to aeter IgG S (I I ) 8. Conversion of galvanoeter in to volteter V R G I g g 9. Magnetic dipole oent M l I g current for full scale deflection in galvanoeter (apere) n nuber of scale division in galvanoeter K figure of erit (apere / div) S shunt resistance (oh) I g current for full scale deflection in galvanoeter (apere) G galvanoeter resistance (oh) I total current (apere) R resistance to be connected in series (oh) I g current for full scale deflection in galvanoeter (apere) G galvanoeter resistance (oh) V potential difference to be easured (volt) M Magnetic dipole oent (apere eter ) pole strength (apere eter) l agnetic length (eter) 3. Force between two agnetic poles 1 F π 4 r 31. Magnetic field strength at a point on axial line of a bar agnet Md B1 4 π (d l ) M when l << d,b1 3 4 π d 3. Magnetic field strength at a point on equatorial line of a bar agnet M B 3/ 4 π (d + l ) F force (newton) 1 and pole strength (apere eter) r distance (eter) B 1 agnetic field strength (tesla) M agnetic oent (apere eter ) l length of the bar agnet (eter) d distance of the point fro the bar agnet (eter) B agnetic field strength (tesla) M agnetic oent (apere eter ) l length of the bar agnet (eter)
M when l << d,b 3 4 π d d distance of the point fro the bar agnet (eter) 33. Magnetic oent of the current loop M NIA NIAn ˆ M agnetic oent (apere eter ) A area (eter ) N nuber of turns 34. Torque acting on a agnetic dipole τ MBsin θ ˆn unit vector M agnetic dipole oent (apere eter ) θ angle between direction of dipole axis and agnetic field (degrees) 35. Potential energy of a dipole in a agnetic field U MB(cos θ cos θ ) 1 τ torque (newton eter) U Potential energy (joule) θ 1, θ angles (degrees) M agnetic dipole oent (apere eter ) 36. Declination θ angle between agnetic eridian and geographic eridian 37. Magnetic eleents of earth H R cos δ V R sinδ R H + V tan δ V /H H horizontal coponent (tesla) V vertical coponent (tesla) R resultant field of earth (tesla) δ angle of dip (degrees) 38. When vertical plane carrying agnetic needle is turned through angle θ then apparent value of angle of dip V V tan δ tan δ ' H' Hcos θ cos θ H horizontal coponent (tesla) H horizontal coponent in the direction of agnetic needle (tesla) V vertical coponent (tesla) δ angle of dip (degrees)
δ ' apparent value of angle of dip (degrees) 39. Tangent law F Htanθ 4. Magnetic oent of an ato due to revolving of electron eh M n( ) n B 4π eh where B 4 π θ angle through which agnetic needle is turned (degrees) F Field intensity (tesla) H Field intensity (tesla) θ angle with H (degrees) M agnetic oent (apere eter ) B Bohr agneton (apere eter ) n nuber of orbit ass of electron (kg) h Planck s constant (joule second) 41. B H I H r B (H + I) 1 + r e charge of electron (coulob) pereability (tesla apere -1 ) H agnetic field intensity (apere eter -1 ) agnetic susceptibility I agnetic oent/volue (apere eter -1 ) r relative pereability pereability of free space (tesla apere -1 ) 4. Curie law C T 43. Energy loss / volue / cycle area of IH loop agnetic susceptibility C constant T teperature ( K) Energy loss (joule) Volue (eter 3 )