1 Ch: lectromagnetic nduction Class X Physics Chater Notes Magnetic Flux Magnetic flux through a lane of area da laced in a uniform magnetic field B = B.dA f the surface is closed, then B. d.a 0 This is because magnetic lines of force are closed lines and free magnetic oles do not exist. lectromagnetic nduction: Faraday s Law a). b). First Law: whenever there is a change in the magnetic flux linked with a circuit with time, an induced emf is roduced in the circuit which lasts as long as the change in magnetic flux continues. Second Law: d nduced emf, Lenz s Law The direction of the induced emf or current in the circuit is such that it ooses the cause due to which it is roduced, so that, d N
N No. of turns in coil Lenz s law based on energy conservation. MF Current and Charge nduced in the Circuit a). b). nduced emf nduced current d N N 1 t N d N 1 Charge deends only on net change in flux does not deends on time. t mf nduced Due to Linear Motion of a Conducting od in a Uniform Magnetic Field. v B f e, v and B are erendicular to each other then Bv nduced MF Due to otation of a Conducting od in a Uniform Magnetic Field 1 B Bn BAn Where n is the frequency of rotation of the conducting rod nduced MF Due to otation of a Metallic Disc in a Uniform Magnetic Field 1 OA B B n BAn nduced MF, Current and nergy Conservation in a ectangular Loo Moving in a Non Uniform Magnetic Field with a Constant Velocity i) Net increase in flux crossing through the coil in time Δt B B v t 1
3 ii) iii) iv) mf induced in the coil B B v 1 f the resistance of the coil is, then the current induced in the coil B1 B v esultant force acting on the coil F B B towards left 1 v) The work done against the resultant force vi) v W B1 B t joule nergy sulied in this rocess aears in the form of heat energy in the circuit. nergy sulied due to flow of current in time Δt H = ² Δt Or v H B1 B t joule Or H = W otation of ectangular Coil in a Uniform Magnetic Field a) Magnetic flux linked with coil BAN cos BAN cos t b) mf induced in the coil d BA N sint 0 sin t c) Current induced in the coil BAN sin t 0 sin t d) Both mf and current induced in the coil are alternating Self nduction and Self nductance (L)
4 On changing the current in a coil, an induced e.m.f. is roduced in the coil then the henomenon is called self in induction i) or L ii) or L d L where L is a constant, called self inductance or coefficient of self induction. Or L d / iii) iv) Self inductance of a circular coil 0 0 µ N µ N A L Self inductance of a solenoid µ 0N A L v) Two coils of self inductances L 1 and L, laced far away (i.e., without couling) from each other. a For series combination: L = L 1 + L.. L n b For arallel combination: 1 1 1 1... L L L L 1 n Mutual nduction and Mutual nductance a) On changing the current in one coil, if the magnetic flux linked with a second coil changes and induced e.m.f. is roduced in that coil, then this henomenon is called mutual induction. b) 1 or M1 Or M 1 d d 1 c) M
5 Or M d / 1 d) M 1 = M 1 = M e) Mutual inductance two coaxial solenoids µ 0N1N A M f) f two coils of self inductance L 1 and L are wound over each other, the mutual inductance is given by M K L L 1 Where K is called couling constant. g) For two coils wound in same direction and connected in series L = L 1 + L + M For two coils wound in oosite direction and connected in series L = L 1 + L M For two coils in arallel L 1 L1L M L L M nergy Stored in an nductor nergy stores in the form of M.F. U B 1 L max Magnetic energy density u B B µ 0
6 ddy Current When a conductor is moved in a magnetic field, induced currents are generated in the whole volume of the conductor. These currents are called eddy currents. Transformer a) t is a device which changes the magnitude of alternating voltage or current. b) s ns K n c) s ns (For ideal transformer) n d) n an ideal transformer: = s s or P in = P out e) n ste down transformer: n s > n or K > 1 s > and s < f) n ste down transformer: n s < n or K < 1 s < and s > g) fficiency Pout 100% P in Generator or Dynamo t is a device by which mechanical energy is converted into electrical energy. t is based on the rincile of.m.. AC Generator t consists of field magnet, armature, sli rings and brushes. DC Generator t consists of field magnet, armature, commutator and brushes. Motor t is a device which converts electrical energy into mechanical energy.
7 Back emf e Current flowing in the coil i a e b Or = e b + i a Where is the resistance of the coil. Out ut Power = i a e b fficiency eb 100%