Motion of Charge at Boundary of Two Magnetic Fields — JEE in 59 Sec 🔥

 

❓ Concept

🎬 Motion of Charge at Boundary of Two Magnetic Fields — Concept in 59 Sec

Ek charged particle uniform magnetic field mein gaya —
👉 circular motion start 🔄

Par jaise hi particle boundary cross karta hai
aur magnetic field change hoti hai,
👉 radius bhi change ho jaata hai!

Ab sawal yeh hota hai:
Net displacement kaise aur kyun aata hai? 🔥

---

🖼️ Concept Image

---

✍️ Short Explanation

Yeh question formula-based nahi,
pure concept + geometry ka test hota hai.

Agar tum radius–bending logic samajh gaye,
toh answer automatically build ho jaata hai 😎

---

🔹 Step 1 — Magnetic Force = Circular Motion (FOUNDATION 💯)**

Jab charge $q$, speed $v$ ke saath
magnetic field $B$ ke perpendicular move kare:

$$qvB = \frac{mv^2}{r}$$

So radius:

$$r=\frac{mv}{qB}$$

📌 Direct observations:

• $B$ ↑ ⇒ $r$ ↓ (particle zyada bend karega)

• $B$ ↓ ⇒ $r$ ↑ (particle kam bend karega)

---

🔹 Step 2 — Two Regions = Two Circular Arcs

Interface ke dono sides par:

• Region 1 → magnetic field $B_1$

• Region 2 → magnetic field $B_2$

So radii:

$$r_1\propto \frac{1}{B_1},r_2\propto \frac{1}{B_2}$$

Particle:

• Boundary par enter karta hai

• Pehle ek circular arc trace karta hai

• Phir dusre region mein different radius ka arc

👉 Same particle, same speed — bas curvature change.

---

🔹 Step 3 — Speed Constant Rehti Hai (VERY IMPORTANT 🔥)**

Magnetic force:

• Velocity ke perpendicular hota hai

• Work nahi karta ❌

So:

• Kinetic energy constant

• Speed constant

• Sirf direction change hoti hai

📌 Isliye radii ka formula simple rehta hai.

---

🔹 Step 4 — Interface = Common Reference Line

Key geometric idea 👇

• Dono circular arcs interface se start hote hain

• Aur interface par hi wapas aate hain

Matlab:

• Net displacement boundary ke perpendicular nahi

• Sirf boundary ke parallel hota hai

👉 Yeh sideways shift
r₁ aur r₂ ke difference se aata hai.

(No calculation here — concept only 😉)

---

🔹 Step 5 — Final Golden Idea (REMEMBER ⭐)**

Magnetic field change ⇒ radius change ⇒ sideways shift

• Stronger field ⇒ tighter circle

• Weaker field ⇒ broader circle

• Dono arcs ka bending mismatch
  👉 Net lateral displacement create karta hai

🧠 One-line memory:

B badla ⇒ r badla ⇒ path shift hua

---

⭐ Golden Summary Box

• Magnetic field ⇒ circular motion

• Radius $r \propto 1/B$
  

• Speed constant (no work by magnetic force)

• Two regions ⇒ two arcs

• Net displacement parallel to interface

• Depends only on $r_1$ and $r_2$

---

✅ Final Takeaway

Aise questions mein:

• Equation kam

• Diagram + intuition zyada kaam karti hai

Is concept ko pakad liya,
👉 Magnetic interface ke saare JEE questions 1 minute mein clear 🚀