Questions: Magnetism and Matter

Q1. Why does the axial field of a short bar magnet equal twice the equatorial field at the same distance?

Answer (English): On the axis both poles of the magnet produce fields pointing the same way, so their contributions add. On the equatorial line the two fields have equal magnitude but point in directions that make an angle with each other, and their components along the axis add only partly. Working out the geometry for a short magnet gives (mu0/4pi)(2m/r cubed) on the axis and (mu0/4pi)(m/r cubed) on the equator, so the axial field is twice as large. Both fall as the inverse cube because the two poles are close together, and their leading effects partly cancel.

Hinglish: Axis par dono poles ke field ek hi direction mein hote hain isliye jud jate hain, jabki equatorial line par unke components sirf partly add hote hain. Short magnet ke liye geometry se axis par (mu0/4pi)(2m/r^3) aur equator par (mu0/4pi)(m/r^3) milta hai, isliye axial field do guna hai. Dono r^3 ke inverse se girte hain kyunki poles paas paas hote hain aur unka leading effect partly cancel hota hai.

Q2. Define the magnetic elements of the earth and relate them.

Answer (English): The earth's magnetic field at a place is described by three numbers. Declination is the angle between the magnetic meridian and the geographic meridian. The angle of dip is the angle the total field makes with the horizontal. The horizontal component is B_H = B cos delta and the vertical component is B_V = B sin delta, where B is the total field and delta is the dip. The three relations tan delta = B_V/B_H, B = square root of (B_H squared + B_V squared), and B_H = B cos delta connect them. At the magnetic equator the dip is zero and the field is horizontal; at the magnetic poles the dip is 90 degrees and the field is vertical.

Hinglish: Teen magnetic elements hain: declination (magnetic aur geographic meridian ka angle), dip delta (field ka horizontal se angle) aur horizontal component B_H. B_H = B cos delta, B_V = B sin delta, tan delta = B_V/B_H. Magnetic equator par dip zero hota hai aur field horizontal, poles par dip 90 degree aur field vertical. Total field B = square root(B_H^2 + B_V^2) se milta hai.

Q3. What is magnetisation and how is it related to magnetic intensity?

Answer (English): Magnetisation is the magnetic moment per unit volume of a material, M = m_net/V, measured in ampere per metre. Magnetic intensity H is the applied field expressed as B_0/mu0, where B_0 is the field that would exist in the absence of the material. Inside the material the flux density is B = mu0(H + M). The susceptibility chi = M/H measures how strongly the material responds, and the relative permeability is mur = 1 + chi. A large chi means the material is easily magnetised and draws field lines into itself.

Hinglish: Magnetisation M magnetic moment per unit volume hota hai, M = m/V, unit A/m. Magnetic intensity H = B0/mu0 hota hai jahan B0 bahar ka field hai. Material ke andar B = mu0(H+M). Susceptibility chi = M/H batata hai material kitna respond karta hai, aur relative permeability mur = 1 + chi. Bada chi matlab material aasani se magnetise hota hai aur field lines andar kheenchta hai.

Q4. Distinguish between diamagnetic, paramagnetic and ferromagnetic materials.

Answer (English): A diamagnetic material has a small negative susceptibility, a relative permeability just below one, and is weakly repelled by a magnet; bismuth and copper are examples. A paramagnetic material has a small positive susceptibility, a permeability just above one, and is weakly attracted; aluminium and oxygen are examples, and its susceptibility falls with temperature as 1/T. A ferromagnetic material has a very large positive susceptibility, a permeability of the order of a thousand, and is strongly attracted; iron, cobalt and nickel are examples, and it becomes paramagnetic above the Curie temperature. The difference comes from the arrangement of atomic moments: none in a diamagnet, random permanent moments in a paramagnet, and aligned domains in a ferromagnet.

Hinglish: Diamagnetic ka chi chhota negative, mur ek se thoda kam, magnet se weak repulsion, jaise bismuth aur copper. Paramagnetic ka chi chhota positive, mur ek se thoda zyada, weak attraction, jaise aluminium aur oxygen; iska chi 1/T se girta hai. Ferromagnetic ka chi bahut bada positive, mur hazaar ke order ka, strong attraction, jaise iron, cobalt, nickel; Curie temperature ke baad woh paramagnetic ban jata hai. Farq atomic moments ke arrangement se aata hai: diamagnet mein permanent moment nahi, paramagnet mein random moments, ferromagnet mein aligned domains.

Q5. What is hysteresis and what does the area of the loop represent?

Answer (English): When a ferromagnetic material is magnetised through a cycle, the graph of B against H does not retrace itself; it forms a closed loop called the hysteresis loop. The value of B left when H returns to zero is the retentivity, and the reverse field needed to reduce B to zero is the coercivity. The area enclosed by the loop equals the energy dissipated as heat per unit volume in one complete cycle. A soft magnetic material has a narrow loop, so the loss is small and it is used for transformer cores and electromagnets; a hard magnetic material has a wide loop, so it keeps its magnetisation and is used for permanent magnets.

Hinglish: Ferromagnetic material ko cycle mein magnetise karne par B aur H ka graph wapas same raste par nahi aata, ek closed hysteresis loop banta hai. H zero karne par bacha hua B retentivity hai, aur B ko zero karne ke liye chahiye reverse field coercivity hai. Loop ka area ek cycle mein heat ke roop mein kharch hui energy per unit volume deta hai. Soft iron ka loop patla hota hai isliye transformer core aur electromagnet ke liye, aur steel ka loop chauda hota hai isliye permanent magnet ke liye use hota hai.

Q6. State Gauss's law for magnetism and explain what it rules out.

Answer (English): Gauss's law for magnetism says that the flux of B out of a closed surface adds up to zero. In symbols, the surface integral of B over a closed surface vanishes. The law rules out isolated magnetic poles, called magnetic monopoles, because a monopole inside a closed surface would give a nonzero net flux. Instead, magnetic field lines are closed loops: whatever enters a closed surface must leave it.

Hinglish: Gauss ka magnetism law kehta hai ki kisi bhi closed surface se net magnetic flux zero hota hai. Iska matlab closed surface par B ka surface integral zero hai. Ye law magnetic monopole ko rule out karta hai, kyunki surface ke andar monopole ho to flux nonzero hota. Magnetic field lines closed loops hote hain: jo andar jata hai woh bahar bhi aata hai. Bar magnet ya solenoid ke liye bhi har closed surface se net flux zero hi rehta hai.

Q7. How is the magnetic moment of a current loop and a solenoid defined?

Answer (English): A planar current loop carrying current I and enclosing area A has a magnetic moment m = IA, directed along the normal to the loop with the sense given by the right hand rule. A solenoid of N turns, each of area A, carrying current I has m = NIA because the contributions of all the turns add. The unit of magnetic moment is ampere metre squared. A solenoid behaves like a bar magnet of the same moment: its field on the axis at a large distance is (mu0/4pi)(2m/r cubed), and inside a long solenoid the field is nearly uniform at B = mu0 n I, where n is the number of turns per unit length.

Hinglish: Planar current loop ka magnetic moment m = IA hota hai, direction loop ke normal ke along right hand rule se milti hai. Solenoid mein N turns hote hain, har ek ka area A, isliye m = NIA. Iska unit A m^2 hai. Solenoid same moment wale bar magnet jaisa behave karta hai: door axis par field (mu0/4pi)(2m/r^3) hota hai, aur lambe solenoid ke andar field lagbhag uniform B = mu0 n I hota hai.

Q8. A magnet is in a uniform field. When is the torque maximum and when is the potential energy minimum?

Answer (English): The torque is tau = mB sin theta, so it is maximum when the angle between m and B is 90 degrees, and zero when the magnet is along or against the field. The potential energy is U = -mB cos theta, so it is minimum at minus mB when m is parallel to B, which is the stable equilibrium.

Hinglish: Torque tau = mB sin theta hai, isliye jab m aur B ke beech 90 degree ho tab maximum hota hai, aur jab magnet field ke along ya against ho tab zero. Potential energy U = -mB cos theta hai, jo m parallel hone par minimum (-mB) hoti hai, aur yahi stable equilibrium hai; antiparallel par maximum (+mB), woh unstable equilibrium hai. Dono positions par torque zero hota hai, par sirf parallel wali stable hai kyunki antiparallel se thoda hilane par torque use door dhakelta hai.

Q9. Why does a paramagnetic material obey Curie's law while a ferromagnet does not?

Answer (English): Thermal motion opposes that alignment, and the balance gives a susceptibility proportional to 1/T, which is Curie's law. In a ferromagnet the atomic moments are already aligned inside domains, so the response is not a simple competition between field and thermal motion; the domains grow and rotate as the field changes, giving a large and nonlinear magnetisation that does not follow 1/T. Only above the Curie temperature, when the domains break up, does the ferromagnet become paramagnetic and obey Curie's law.

Hinglish: Paramagnet mein atomic moments permanent hote hain par random, field unhe sirf partly align karta hai, aur thermal motion virodh karta hai, isliye chi 1/T ke proportional hota hai (Curie law). Ferromagnet mein moments domains ke andar pehle se aligned hote hain, isliye response field aur temperature ki simple competition nahi hai; domains badhte aur ghoomte hain, jisse bada nonlinear magnetisation milta hai. Curie temperature ke upar domains toot jate hain tab hi woh paramagnet ban kar Curie law follow karta hai.

Q10. Why is soft iron used for an electromagnet and steel for a permanent magnet?

Answer (English): The choice follows the shape of the hysteresis loop. Soft iron has high permeability and low coercivity, so it is easily magnetised by a small current and loses its magnetism almost completely when the current stops; its narrow loop also means little energy is lost in each cycle, which matters for transformer cores. Steel has lower permeability but high retentivity and high coercivity, so once magnetised it keeps a strong field and resists demagnetisation by stray fields or by a moderate reverse field, which is exactly what a permanent magnet needs.

Hinglish: Chunav hysteresis loop ke shape se hota hai. Soft iron ka permeability zyada aur coercivity kam hoti hai, isliye chhote current se magnetise ho jata hai aur current band hone par magnetism chhod deta hai; patla loop matlab kam energy loss, isliye transformer core ke liye sahi. Steel ka retentivity aur coercivity zyada hoti hai, isliye magnetise hone ke baad strong field banaye rakhta hai aur stray fields se demagnetise nahi hota, yahi permanent magnet ke liye chahiye. Electromagnet ke liye quick change, permanent magnet ke liye lasting magnetism.

Quiz below: five questions on the dipole field, the earth's elements, magnetic classes and hysteresis. Check the torque and energy signs before you start.