Questions: Electromagnetic Induction

Q1. Define magnetic flux and state its SI unit.

Answer (English): The magnetic flux through a surface is the number of magnetic field lines crossing it, and for a plane area A in a uniform field B it is phi = BA cos theta, where theta is the angle between the field and the area vector. The flux is maximum when the surface is perpendicular to the field and zero when it is parallel. The SI unit is the weber, which is one tesla metre squared. Flux is a scalar with a sign that depends on the chosen normal, and for a curved surface or a non-uniform field it is found by summing B dot dA over the surface.

Hinglish: Magnetic flux surface se guzarne wali field lines ki ginti hai; plane area A ke liye phi = BA cos theta, jahan theta field aur area vector ka angle hai. Surface field ke perpendicular ho to flux maximum aur parallel ho to zero. Unit weber = tesla metre squared. Flux scalar hai par normal ke choice se sign badal sakta hai; curved surface ke liye B dot dA ka sum lete hain.

Q2. State Faraday's law of electromagnetic induction.

Answer (English): Faraday's law says that the emf induced in a circuit is set by how fast the flux through it changes, taken with a minus sign that fixes the direction by Lenz's law. For a coil of N turns the emf is minus N times the rate of change of flux linkage. The law covers all the ways the flux can change, whether the field itself changes, or the area changes, or the orientation of the loop changes. In every case the magnitude of the emf equals the rate at which flux is being cut or linked, and a steady flux produces no emf at all.

Hinglish: Faraday ka law kehta hai ki circuit mein induced emf flux ke change ki rate ke barabar hota hai, aur minus sign Lenz ke hisaab se direction batata hai. N turns wali coil ke liye emf minus N d(phi)/dt hota hai. Flux badalne ke saare tarike isi law mein aate hain: field badle, area badle ya loop ka orientation badle. Steady flux se koi emf nahi milta.

Q3. State Lenz's law and explain how it follows from conservation of energy.

Answer (English): Lenz's law says the induced current flows in a direction that opposes the change in flux producing it. When a magnet is pushed towards a coil, the coil's induced field repels the magnet, so the person pushing has to do work; when the magnet is pulled away, the coil attracts it back and again resists the motion. That work appears as the electrical energy dissipated in the coil. If the induced current instead helped the motion, the magnet would speed up with no work input and energy would be created, which is impossible. So the opposition required by the law is the same statement as conservation of energy.

Hinglish: Lenz ka law kehta hai induced current woh direction leta hai jo flux ke change ka virodh kare. Magnet ko coil ke paas dhakelne par coil usko repel karti hai, isliye dhakelne wale ko kaam karna padta hai; door kheenchne par woh attract karke phir virodh karti hai. Yahi kaam electrical energy ban jata hai. Agar current madad karta to magnet bina kaam ke tez hota aur energy create hoti, jo mumkin nahi. Isliye Lenz ka virodh hi energy conservation hai.

Q4. Derive the motional emf for a rod moving on rails.

Answer (English): A rod PQ of length l slides on rails in a uniform field B perpendicular to the plane of the rails, with speed v. The area of the circuit increases at the rate l v, so the flux changes at the rate B l v. Faraday's law then gives the emf as B l v. The same result comes from the magnetic force on the free electrons in the moving rod, which pushes them to one end and sets up an electric field along the rod. If the circuit resistance is R, the current is B l v / R, the magnetic force on the rod is B I l and the power dissipated is (B squared l squared v squared)/R.

Hinglish: Lambai l ka rod rails par speed v se chalta hai aur field B plane ke perpendicular hai. Circuit ka area l v ki rate se badhta hai, isliye flux B l v ki rate se badalta hai, aur Faraday se emf B l v milta hai. Yahi result rod ke free electrons par magnetic force se bhi milta hai, jo unhe ek end par dhakel kar emf banati hai. Resistance R ho to current Blv/R, rod par force BIl aur power B^2l^2v^2/R hoti hai.

Q5. What are eddy currents? Give two uses and one way of reducing their loss.

Answer (English): Eddy currents are induced currents that circulate in the bulk of a conductor when the magnetic flux through it changes, either because the field varies with time or because the conductor moves through the field. Two uses are magnetic braking, where the eddy currents oppose the motion and slow a train or a galvanometer coil, and induction heating, where the currents heat a metal in a furnace or in a cooking hob. The loss in a transformer core is reduced by making the core from thin insulated sheets called laminations, which cut the paths available to the eddy currents and so lower the energy dissipated as heat.

Hinglish: Eddy currents solid conductor ke andar induce hui currents hain jo flux badalne par circulate karti hain. Do uses: magnetic braking, jahan ye motion ka virodh karke train ya galvanometer coil ko dheema karti hain, aur induction heating, jahan ye metal ko garam karti hain. Transformer core mein loss kam karne ke liye core ko patli insulated sheets ki laminations se banate hain, jo eddy currents ke raaste todti hain.

Q6. Define self inductance and write the expression for a long solenoid.

Answer (English): Self inductance is the property of a coil by which a change in its own current induces an emf in it. The induced emf is minus L times the rate of change of current, so L equals the flux linkage per unit current. For a long solenoid of N turns, length l and cross sectional area A, the field inside is mu0 n I with n equal to N/l, the flux per turn is mu0 n I A, and the flux linkage is N times that. Dividing by the current gives L = mu0 N squared A / l, which can also be written mu0 n squared A l, where n is the number of turns per unit length. The unit is the henry.

Hinglish: Self inductance coil ki woh property hai jisse apne current ke change se apne hi andar emf induce hota hai. Induced emf minus L di/dt hota hai, isliye L flux linkage per unit current hai. Lambe solenoid ke liye andar B = mu0 n I, per turn flux mu0 n I A aur total flux linkage N guna. Current se divide karke L = mu0 N^2 A / l milta hai, ya mu0 n^2 A l, jahan n turns per unit length hai. Unit henry hai.

Q7. Define mutual inductance for two coils and give its unit.

Answer (English): Mutual inductance of a pair of coils is the flux linkage in one coil produced by unit current in the other. When the current in the first coil changes at rate di/dt, an emf equal to minus M di/dt appears in the second coil. For two coaxial solenoids of length l and area A with N1 and N2 turns, the flux per turn in the second coil is mu0 N1 I1 A / l, and multiplying by N2 and dividing by I1 gives M = mu0 N1 N2 A / l. The unit is the henry, and the value depends on the geometry, separation, orientation and the core material of the two coils, not on the currents themselves.

Hinglish: Do coils ki mutual inductance M itni hoti hai ki ek coil mein unit current doosri coil mein kitna flux linkage banata hai. Pehli coil ka current di/dt se badle to doosri mein emf minus M di/dt aata hai. Coaxial solenoids ke liye M = mu0 N1 N2 A / l. Unit henry. M coil dono ki geometry, doori, orientation aur core par depend karta hai, currents par nahi.

Q8. Where is the energy stored in an inductor and what is its expression?

Answer (English): The energy in an inductor is stored in its magnetic field, not in the wire. While the current grows from zero to I, the source does work against the induced emf, and the energy stored comes out as half L I squared. For a solenoid this can be written in terms of the field: substituting L = mu0 n squared A l and I = B/(mu0 n) gives the energy as B squared times the volume divided by 2 mu0, so the energy density is B squared / (2 mu0). That expression is general and gives the energy carried by any magnetic field, which is why the magnetic field of a wave can transport energy.

Hinglish: Inductor ki energy uske magnetic field mein store hoti hai. Current zero se I tak badhne ke dauran source induced emf ke against kaam karta hai, aur energy half L I squared hoti hai. Solenoid ke liye L aur B ke formulas daalne par energy B^2 x volume / (2mu0) milti hai, yaani energy density B^2/(2mu0). Ye expression har magnetic field ke liye chalta hai, isliye wave ka field bhi energy le jata hai.

Q9. Explain the working of an AC generator.

Answer (English): An AC generator consists of a coil of N turns and area A rotating with angular speed omega in a uniform magnetic field B, with the coil axis perpendicular to the field. The flux linkage at time t is N B A cos omega t, so the emf is N B A omega sin omega t. The output therefore alternates sinusoidally, with peak value N B A omega, and it reverses direction every half rotation. Slip rings and brushes carry the current to the external circuit. The emf is increased by using more turns, a larger area, a stronger field or a faster rotation, and this is why generators use many turns and strong electromagnets rather than a simple loop.

Hinglish: AC generator mein N turns aur area A ki coil uniform field B mein angular speed omega se ghoomti hai, coil ka axis field ke perpendicular hota hai. Flux linkage N B A cos omega t hota hai, isliye emf N B A omega sin omega t milta hai. Output sinusoidal alternate hota hai, peak N B A omega, aur direction har aadhe rotation mein badal jata hai. Slip rings aur brushes current ko circuit tak pahunchate hain. Emf badhane ke liye zyada turns, bada area, strong field ya tez rotation use karte hain.

Q10. What is the difference between self and mutual inductance?

Answer (English): Self inductance describes the emf induced in a coil by a change in its own current, and it depends only on that coil's geometry, the number of turns and the core. Mutual inductance describes the emf induced in one coil by a change in the current of a second, coupled coil, and it depends on the geometry of both coils and on how well their flux links. Self inductance gives the energy stored in the coil, half L I squared, while mutual inductance is the basis of the transformer. Both are measured in henry, and for two identical coaxial solenoids the mutual inductance is the same whichever coil carries the changing current.

Hinglish: Self inductance khud coil ke current ke change se usme emf inducer karti hai, aur ye sirf us coil ki geometry, turns aur core par depend karti hai. Mutual inductance ek coil ke current ke change se doosri coil mein emf inducer karti hai, aur ye dono coils ki geometry aur flux linkage par depend karti hai. Self inductance se energy half L I squared milti hai, mutual inductance transformer ka basis hai. Dono ka unit henry hai, aur identical coaxial solenoids mein M dono taraf se same hota hai.

Quiz below: five questions on Faraday's law, Lenz's law, motional emf, inductance and the generator. Write the law name with every direction answer.