Unit-2: Steady Magnetic Field

For: B.E. / B.Tech (ECE, EE, EEE)

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1. Steady Magnetic Field

Steady magnetic field wo magnetic field hota hai jo time ke sath change nahi hota।
Ye normally DC current ke karan produce hota hai।

👉 Example: current carrying conductor, solenoid, toroid.

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2. Magnetic Field Strength (H)

Magnetic field strength H magnetic field ki intensity batata hai।

• Symbol: H

• Unit: Ampere/meter (A/m)

H mainly current aur conductor ki geometry par depend karta hai।

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3. Magnetic Flux Density (B)

Magnetic flux density B actual magnetic field ko show karta hai jo medium ke andar hota hai।

• Symbol: B

• Unit: Tesla (Wb/m²)

Relation

B = μH

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4. Magnetomotive Force (MMF)

MMF magnetic circuit me flux ko drive karne wali force hoti hai।

Formula

MMF = N × I

• N = number of turns

• I = current

👉 MMF electric circuit ke EMF ke equivalent hota hai।

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5. Ampere’s Circuital Law

Statement

Closed path ke along magnetic field intensity ka line integral enclosed current ke equal hota hai।

Equation

∮ H · dl = I

👉 Ye law symmetrical structures ke liye useful hai।

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6. Ampere’s Law in Differential Vector Form

Magnetic field ka point form differential equation se show kiya jata hai।

Equation

∇ × H = J

Where J = current density

👉 Ye Maxwell’s equations ka ek part hai।

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7. Permeability (μ)

Permeability batata hai ki koi material magnetic field ko kitna allow karta hai।

Formula

μ = B / H

Types of Materials

• Diamagnetic

• Paramagnetic

• Ferromagnetic

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8. Energy Stored in a Magnetic Field

Magnetic field me energy store hoti hai, jaise inductor me।

Energy Density

w = ½ B H

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9. Ampere’s Law for a Current Element (Biot-Savart Law)

Statement

Current element ke karan magnetic field produce hota hai jo distance aur current par depend karta hai।

Formula

dB = (μ₀ / 4π) × (I dl × r̂) / r²

👉 Any shape ke conductor ke liye valid hai।

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10. Magnetic Vector Potential (A)

Magnetic vector potential A ek vector quantity hai jisse magnetic field express kiya jata hai।

Relation

B = ∇ × A

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11. Boundary Conditions for Magnetic Fields

Boundary conditions batati hain ki do media ke interface par magnetic field ka behavior kaisa hota hai।

• Tangential component of H continuous

• Normal component of B continuous

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12. Analogies Between Electric and Magnetic Fields

Electric Field	Magnetic Field
Electric field (E)	Magnetic field (H)
Flux density (D)	Flux density (B)
Permittivity (ε)	Permeability (μ)
Gauss’s Law	Ampere’s Law

👉 Ye analogy concepts ko easily samajhne me madad karti hai