Magnetic Susceptibility Trick: Field Change in Solenoid ⚡

❓ Concept

🎬 Solenoid + Magnetic Material = New Magnetic Field | Concept in 59 Sec

Solenoid ke andar vacuum/air ki jagah
agar magnesium ya koi magnetic material bhar diya…

👉 Magnetic field badal jaati hai 🧲
Par kyun, aur kitni?
Yeh concept JEE mein baar-baar aata hai 🔥

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🖼️ Concept Image

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✍️ Short Explanation

Is type ke questions mein calculation kam
aur definition zyada important hoti hai.

Agar tum μ, μr aur χ ka relation pakad loge,
toh answer seconds mein nikal jaata hai 😎

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🎯 HOOK (Write & Read First)

“Agar solenoid ke andar vacuum ki jagah magnesium bhar diya…
toh magnetic field badh jaati hai — par kyun aur kitni?” 🧲🤔

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🔹 Step 1 — Magnetic Field of a Solenoid (in Air / Vacuum)**

Long solenoid ke liye:

$$B_0={\mu }_{0}nI$$

Yahaan:

• $n$ = turns per unit length

• $I$ = current

• $\mu_0$ = permeability of free space

📌 Yeh reference field hota hai (without material).

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🔹 Step 2 — When a Magnetic Material is Inserted

Material daalne par:

• Medium ki permeability change hoti hai

• Magnetic field becomes:

$$B=\mu nI$$

Where:

$$\mu ={\mu }_0{\mu }_r$$

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🔹 Step 3 — Relation Between Relative Permeability and Susceptibility (VERY IMPORTANT 🔥)**

Direct JEE formula:

$${\mu }_r=1+\chi$$

Yahaan:

• $\chi$ = magnetic susceptibility

• Paramagnetic materials (like Mg) ke liye
  $\chi$ small & positive hota hai

📌 JEE questions almost hamesha χ directly dete hain.

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🔹 Step 4 — New Magnetic Field Expression

Substitute $\mu_r$:

$$B_{\text{new}}={\mu }_0(1+\chi )nI$$

Compare with:

$$B_{\text{old}}={\mu }_{0}nI$$

So:

$$\boxed{{\displaystyle B_{\text{new}}=B_{\text{old}}(1+\chi )}}$$

👉 Field multiply ho jaati hai $(1+\chi)$ se.

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🔹 Step 5 — Percentage Increase Shortcut (EXAM GOLD ⭐)**

Fractional increase:

$$\frac{\mathrm{\Delta }B}{B_{\text{old}}}=\chi$$

So:

$$\boxed{{\displaystyle \mathrm{\%}\text{ increase in }B=\chi \times 100}}$$

📌 Bas susceptibility ko percent mein convert kar do —
answer mil gaya 😄

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⭐ Golden Summary Box

• Solenoid field (air): $B_0=\mu_0 n I$
  

• With material: $B=\mu_0(1+\chi)nI$
  

• Relative permeability: $\mu_r=1+\chi$
  

• Percentage increase in $B$: $\chi \times 100\%$
  

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✅ Final Takeaway

🧠 One-line memory trick

Solenoid + material ⇒ field × (1 + χ)

Is concept ko yaad rakho,
👉 Magnetic susceptibility ke JEE questions free marks ban jaate hain 🚀