Govt. Exams
Entrance Exams
When the magnetic core saturates, further increase in current produces minimal increase in magnetic flux, causing inductance to decrease. This is the saturation effect in magnetic cores.
After acceleration: ½m₁v₁² = q₁V and ½m₂v₂² = q₂V. In magnetic field, r = mv/(qB). r₁/r₂ = (m₁v₁/q₁)/(m₂v₂/q₂) = (4u × √(2eV/4u)/2e)/(u × √(2eV/u)/e) = √(2u/e) × e/(√(2eV) × √(2V/u)) = 2√2:1.
Magnetic energy U = ½LI² where L = μ₀N²A/(2πR) for a toroid. Therefore U = μ₀N²I²A/(4πR). Note: The correct formula is actually U = ½ × μ₀N²I²A/(2πR) = μ₀N²I²A/(4πR).
For a circular arc, B = (μ₀I/4πR) × θ, where θ is in radians. This is derived from the Biot-Savart law integrated over the arc.
Hall voltage V_H = BId/ne·t indicates carrier sign from voltage polarity and carrier density n from magnitude. This dual information makes Hall effect powerful for semiconductor characterization.
For coaxial coils with large separation d >> radius, mutual inductance M ∝ 1/d² due to spreading of magnetic field lines. This is used in wireless power transfer systems.
In a toroid, using Ampere's law on circular path of radius r (inside toroid): B(2πr) = μ₀NI, so B = μ₀NI/2πr. Field varies inversely with distance from toroid center.
For undeflected motion, electric and magnetic forces must balance: qE = qvB, giving E = vB. This is the principle of velocity selector used in mass spectrometers.
For equal perimeter, circle encloses maximum area (isoperimetric inequality). Since magnetic moment m = IA, circular loop with larger area has larger magnetic moment.
