Govt. Exams
In paramagnetic materials, unpaired electrons have permanent magnetic moments that align with external field
Motional EMF arises because free electrons experience Lorentz force F = -e(v × B) as conductor moves through field
r = mv/(eB), so r_e/r_p = (m_e/m_p) = 1/1836 approximately
Mutual inductance M₁₂ = k√(L₁L₂) depends on coil geometry, orientation, and proximity, not on current or resistance
When cut perpendicular to length, magnetic moment is halved. Each piece has half the pole strength or length.
Induced EMF: ε = Bdv, induced current: I = Bdv/R, magnetic force: F = BId = B²d²v/R (opposes motion)
Self-inductance of solenoid: L = μ₀n²V = μ₀(N/L)²AL = μ₀N²A/L
Maximum EMF in rotating coil: ε_max = NABω, where Φ = NBA cos(ωt), so ε = dΦ/dt = NABω sin(ωt)
EMF induced ε = BLv where L is the length of the conductor cutting magnetic field lines and v is the velocity. It depends on all three factors: B, L, and v.
The cyclotron frequency f = qB/(2πm) is independent of velocity. As velocity increases, radius increases but period remains constant (independent of v).
