Govt. Exams
Between the parallel poles of a strong permanent magnet (in the central region), the magnetic field is approximately uniform. However, it becomes non-uniform near the pole edges.
Cyclotron frequency f = qB/(2πm). It depends on q, B, and m, but not on velocity v
Mutual inductance M = k√(L₁L₂), where 0 ≤ k ≤ 1 is the coupling coefficient
Magnetic energy density u = B²/(2μ₀), similar to electric field energy density
Non-uniform field causes net force on the loop due to unequal forces on different sides, plus torque due to magnetic moment
Hall voltage V_H = (1/ne) × (IB/t), proportional to B and I, inversely proportional to carrier concentration n
Perpendicular component causes circular motion, parallel component causes linear motion, resulting in helical path
L = μ₀n²AL, where n = N/l. Self-inductance depends on geometry and material properties, not on current.
Energy stored in inductor: U = ½LI², derived from dW = LI dI integrated from 0 to I
For LR circuit, time constant τ = L/R. Current rises as I = (V/R)(1 - e^(-t/τ))
