An electric dipole of mass m, charge q, and length l is placed in a uniform electric field E = E₀ i.

Описание: An electric dipole of mass m, charge q, and length l is placed in a uniform electric field E = E₀ i. When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be :
(1) 1/2π (√(2ml/qE₀)) (2) 2π (√(ml/qE₀))
(3) 1/2π (√(ml/2qE₀)) (4) 2π (√(ml/2qE₀))

🎥 Video Title: Electric Dipole Oscillations | JEE Mains 2025 PYQ Solved 🔥
📚 Chapter/Topic: Electrostatics | Electric Dipole in Uniform Electric Field
🎯 Exam Focus: JEE Mains 2025 | NEET 2025

📖 In This Video:
In this video, I’ve solved a JEE Mains 2025 Previous Year Question (PYQ) based on the oscillations of an electric dipole placed in a uniform electric field. The problem involves understanding how an electric dipole behaves when slightly displaced from its equilibrium position and determining its time period of oscillation. This problem is a perfect blend of electrostatics and oscillations, making it a must-watch for all JEE and NEET aspirants. I’ve explained the entire concept in a simple and engaging way, focusing on the theory and avoiding complex calculations.

🔥 Key Highlights:
✅ What is an electric dipole, and how does it behave in a uniform electric field?
✅ Understanding the concept of torque and restoring force acting on the dipole.
✅ Deriving the time period of oscillation for the dipole using simple physics principles.
✅ Step-by-step breakdown of the problem without complex formulas.
✅ Tips to approach similar questions in JEE Mains 2025.

Theory and Problem Explanation:
In this problem, we’re dealing with an electric dipole placed in a uniform electric field. Here’s a breakdown of the setup and the solution:

Setup Overview:

An electric dipole consists of two charges +q and -q separated by a distance l.

The dipole is placed in a uniform electric field E = E₀ i.

When the dipole is slightly rotated from its equilibrium position and released, it undergoes oscillations.

We need to find the time period of these oscillations.

Key Concepts:

Electric Dipole in a Uniform Electric Field:

In a uniform electric field, an electric dipole experiences a torque that tries to align it with the field.

The torque is given by: τ = pE sinθ, where p is the dipole moment, E is the electric field, and θ is the angle between the dipole and the field.

Restoring Torque and Oscillations:

When the dipole is slightly displaced from its equilibrium position, the torque acts as a restoring torque, causing the dipole to oscillate.

For small angles, the motion is simple harmonic, and we can use the principles of SHM to find the time period.

Time Period of Oscillation:

The time period (T) of oscillation depends on the moment of inertia (I) of the dipole and the restoring torque.

Using the analogy of a physical pendulum, we can derive the time period as:
T = 2π √(I / pE),
where I is the moment of inertia of the dipole.

Connecting the Dots:

For an electric dipole of length l and mass m, the moment of inertia is I = ml²/12.

Substituting this into the time period formula, we get:
T = 2π √(ml² / (12pE)).

Since p = ql, the final expression for the time period becomes:
T = 2π √(ml / (2qE₀)).

Final Answer:
After analyzing the setup and applying the concepts of electrostatics and oscillations, the time period of oscillation is:
2π √(ml / (2qE₀)).

Why This Problem is Important:
This problem tests your understanding of electric dipoles, torque, and simple harmonic motion, which are crucial topics for JEE Mains and NEET. By solving this problem, you’ll learn how to handle questions that combine multiple concepts, a common trend in competitive exams.

📜 About This Channel:
Welcome to Physics Behind Everything! 🚀 Here, I create highly engaging and educational content for JEE and NEET aspirants. My goal is to make Physics easy and fun for you. From detailed problem-solving videos to motivational shorts, I’ve got everything you need to ace your exams. Don’t forget to subscribe and hit the bell icon to stay updated!

📌 Important Links:
👉 Follow me on Instagram for daily Physics tips, motivation, and updates: Instagram - @physics_behind_everything
👉 Watch my full playlist on Electrostatics: [Insert Playlist Link]


#JEEMains2025 #NEET2025 #Physics #ElectricDipole #Electrostatics #CompetitiveExams #PhysicsBehindEverything #ExamPreparation #PYQs