Formula sheet: Electromagnetic Induction

Electromagnetic Induction12 min readLesson 1 of 6

1.1 Core formulas Quantity Expression Notes Magnetic flux through a plane area phi = B A cos theta theta is the angle between B and the area vector Faraday's law emf = -d(phi)/dt Negative sign gives the direction by Lenz's law Flux through a coil of N turns total flux = N phi the emf becomes -N d(phi)/dt Motional emf, rod moving on rails emf = B l v when B, l and v are mutually perpendicular Rod rotating about one end emf = half B omega l squared B perpendicular to the plane of rotation Coil rotating in a uniform field emf = N B A omega sin omega t peak value N B A omega Self induced emf emf = -L (di/dt) L in henry Self inductance of a solenoid L = mu0 N squared A / l = mu0 n squared A l n is turns per unit length Mutual inductance emf2 = -M (di1/dt) M in henry Mutual inductance of coaxial solenoid and coil M = mu0 N1 N2 A / l same core length and area Energy stored in an inductor U = half L I squared energy of the magnetic field Magnetic energy density u = B squared / (2 mu0) energy per unit volume 1.2 Units to remember The magnetic flux has the unit weber, one weber being one tesla metre squared. The self and mutual inductance have the unit henry, one henry being one weber per ampere or one volt second per ampere. An emf of one volt is induced when the flux through a circuit changes at the rate of one weber per second. 1.3 The three rules that decide the direction Lenz's law says the induced current is in a direction that opposes the change in flux that produced it. The right hand rule converts that opposition into a direction of current for a coil in a field. Flemming's right hand rule gives the direction of induced current when a conductor moves in a field: forefinger along the field, thumb along the motion and the middle finger along the current. All three rules are bookkeeping devices for the same physics, and an exam answer should name the rule used and then state the direction.

Quantity	Expression	Notes
Magnetic flux through a plane area	phi = B A cos theta	theta is the angle between B and the area vector
Faraday's law	emf = -d(phi)/dt	Negative sign gives the direction by Lenz's law
Flux through a coil of N turns	total flux = N phi	the emf becomes -N d(phi)/dt
Motional emf, rod moving on rails	emf = B l v	when B, l and v are mutually perpendicular
Rod rotating about one end	emf = half B omega l squared	B perpendicular to the plane of rotation
Coil rotating in a uniform field	emf = N B A omega sin omega t	peak value N B A omega
Self induced emf	emf = -L (di/dt)	L in henry
Self inductance of a solenoid	L = mu0 N squared A / l = mu0 n squared A l	n is turns per unit length
Mutual inductance	emf2 = -M (di1/dt)	M in henry
Mutual inductance of coaxial solenoid and coil	M = mu0 N1 N2 A / l	same core length and area
Energy stored in an inductor	U = half L I squared	energy of the magnetic field
Magnetic energy density	u = B squared / (2 mu0)	energy per unit volume

ε = - \frac{d Φ}{d t}, Φ = B A cos θ

Faraday's law of induction with the Lenz sign and the definition of magnetic flux

ε = B l v, P = \frac{B ^{2} l ^{2} v ^{2}}{R}

Motional emf of a rod moving on rails and the power dissipated in the loop

L = μ_{0} n^{2} A l, U = \frac{1}{2} L I^{2}, u = \frac{B ^{2}}{2 μ _{0}}

Self inductance of a long solenoid and the energy stored in the magnetic field

in hinglish

Formula sheet ke formulas yaad rakho. Flux phi = BA cos theta hota hai aur uska unit weber hai. Faraday ka law : emf = -d(phi)/dt, aur N turns ke liye emf = -N d(phi)/dt. Lenz ka law kehta hai induced current woh direction leta hai jo flux ke change ka virodh kare. Motional emf ke liye rod rails par chale to emf = Blv, current Blv/R, aur power B^2l^2v^2/R. Rotating rod ke liye emf = half B omega l squared. Coil uniform field mein ghoome to emf = NBA omega sin omega t, aur peak value NBA omega. Self inductance ka formula L = mu0 n^2 A l aur solenoid ka L = mu0 N^2 A / l hota hai, unit henry. Mutual inductance M = mu0 N1 N2 A / l, aur emf2 = -M di1/dt. Inductor mein energy U = half L I squared store hoti hai, aur energy density B^2/(2 mu0) hoti hai. Flemming ka right hand rule direction nikaalne ke liye hai: field, motion aur current ki directions. Exam mein law ka naam likho, formula lagao, phir direction ke liye Lenz ka reason do.