I.E. Irodov Problem 3.41 Solution | Electrostatics

Introduction

Preparing for JEE Advanced requires strong conceptual clarity, and solving problems from I.E. Irodov is one of the best ways to achieve that. In this article, we provide a complete solution to I.E. Irodov Problem 3.41 from Electrostatics with a step-by-step explanation.

This problem focuses on the relationship between electric potential, electric field, and motion of a charged particle, making it highly important for exam preparation.

Concepts Required

To solve I.E. Irodov Problem 3.41, you must understand:

Electric field and potential relation
Motion of charged particles
Energy conservation in electrostatics

The key formula used is:

$E = -\frac{dV}{dz}$ E=−dzdV

This equation shows that the electric field is the negative gradient of potential.

Step-by-Step Solution

Step 1: Analyze the Potential Function

The potential is given as a function of position along the z-axis: $V(z) = f(z)$ V(z)=f(z)

This function determines how the electric field varies in space.

Step 2: Find the Electric Field

Differentiate the potential: $E(z) = -\frac{dV}{dz}$ E(z)=−dzdV

This gives the electric field acting on the particle.

Step 3: Force on the Particle

The force acting on a charge $q$ q is: $F = qE$ F=qE

This determines the acceleration of the particle.

Step 4: Apply Energy Conservation

Since the particle starts from rest:

$qV(z_0) = qV(z) + \frac{1}{2}mv^2$ qV(z0)=qV(z)+21mv2

This equation helps us find velocity at any point.

Step 5: Determine Turning Point

At maximum displacement: $v = 0$ v=0

So, $V(z_0) = V(z_{\text{max}})$ V(z0)=V(zmax)

Solve this equation to find the turning point.

Final Result

The particle moves under the influence of a non-uniform electric field
Its motion is best analyzed using energy conservation
The turning point is obtained when kinetic energy becomes zero

Important Tips

Always include the negative sign in $E = -dV/dz$ E=−dV/dz
Use energy methods instead of force when possible
Carefully apply initial conditions

Why This Problem Matters

Frequently relevant for JEE Advanced level questions
Strengthens concepts of electric potential and motion
Improves analytical problem-solving skills

Conclusion

The I.E. Irodov Problem 3.41 solution is a great example of how multiple electrostatics concepts come together. By mastering this, you’ll be better prepared for advanced physics problems.

Call to Action

📞 Contact: 9811767502
🌐 Website: physicsonlinetutor.com

Get expert guidance for JEE Advanced Physics preparation.