Magnetic Susceptibility Trick — % Increase in B in 60 Seconds! 🔥
❓ Question The percentage increase in magnetic field B B when the space within a current-carrying solenoid is filled with magnesium , given that the magnetic susceptibility of magnesium is χ Mg = 1.2 × 10 − 5 , is equal to ? 🖼️ Question Image ✍️ Short Solution This is a direct concept-based JEE question . No lengthy derivation — just one clean relation between magnetic field and susceptibility. 🔹 Step 1 — Magnetic field inside a solenoid (key idea 🔥)** For a long solenoid: In air (or vacuum) : B 0 = μ 0 n I When filled with a magnetic material : B = μ 0 ( 1 + χ ) n I Here: χ \chi = magnetic susceptibility of the material n n = turns per unit length I I = current 📌 The geometry and current remain the same — only permeability changes. 🔹 Step 2 — Change in magnetic field Increase in magnetic field: Δ B = B − B 0 = μ 0 n I χ So, Δ B B 0 = χ 👉 This is the golden result. 🔹 Step 3 — Percentage increase formula % ...