Скачать или смотреть Electric Field due to a Dipole on Axial Line | Visual Derivation

Deriving the Electric Field due to a Dipole often confuses students because of the vector directions and distance algebra. In this video, we visualize exactly how the fields from positive and negative charges interact on the Axial Line. 🧲

We break down the derivation step-by-step using animations, starting from the definition of the Electric Dipole Moment (
p

​
) to the final approximation for short dipoles. You'll see why the field drops off as 1/r
3
instead of the usual 1/r
2
.

📘 Topics Covered in This Video:

What is an Electric Dipole? (Charges ±q separated by 2a)

Definition of Electric Dipole Moment (
p

​
).

Setting up the diagram for the Axial Position.

Vector analysis: Why the net field points along
p

​
.

Step-by-Step Derivation: Solving the algebra for E
net
​
.

Short Dipole Approximation: The case where r≫a.

⏱️ Timestamps: 0:00 - Introduction to Electric Dipole 0:21 - Electric Dipole Moment (
p

​
) 0:39 - Axial Line Diagram Setup 0:58 - Force Analysis (F
A
​
vs F
B
​
) 1:15 - Mathematical Derivation 1:56 - Short Dipole Approximation (r≫a) 2:07 - Final Formula & Conclusion

📝 Key Formulas:

Dipole Moment:
p

​
=q(2
a

)

Final Axial Field:
E


axial
​
=
4πϵ
0
​

1
​

r
3

2
p

​

​
(for r≫a)

💡 About PHYMICS: Visualizing the invisible laws of the universe. This channel uses Manim (Mathematical Animation Engine) to explain complex Physics concepts through intuition and code.

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