
When an electric dipole $\vec{p}$ is placed in a uniform electric field $\vec{E}$ then at what angle between $\vec{P}$ and $\vec{E}$ the value of torque be maximum?
Answer
161.1k+ views
Hint: As we know torque is used to define a force applied to an object in the given question the force is applied in the form of the electric field. So, on placing the dipole in the electric field, the direction will be clockwise if it is positive, and the direction will be anticlockwise if it is negative. Use this concept to solve the problem.
Formula used:
$ \tau=\vec{p}\times\vec{E}\ sin\theta$
Where; τ = torque
$\vec{p}$ = magnitude of the charges on both the ends/point of the dipole
$\vec{E}$ = Electric field applied on the dipole
ϴ = Angle of rotation of dipole with its axis in presence of electric field
Complete answer:
On both the dipoles, the force will be
$\tau=+q\times\vec{E}\ sin\theta$ (anticlockwise for the one point of the dipole)
$\tau=-q\times\vec{E}\ sin\theta$ (clockwise for the other point of the dipole)
So, the torque acting on the dipole is
$\tau=q\times\vec{E}\ sin\theta$
Since; Since the values of sinϴ are-
As, Sin90˚= 1
So we can see that at an angle of 90˚ the dipole will experience the maximum torque because its value is 1 (maximum).
Thus, the value of torque will be maximum at an angle of 90˚
Note: Torque is a vector quantity it depends on the direction of the force. The distance between the point where force is applied and the point of rotation at the dipole is called an arm. One should know the concept of stable and unstable equilibrium also to understand the question.
Formula used:
$ \tau=\vec{p}\times\vec{E}\ sin\theta$
Where; τ = torque
$\vec{p}$ = magnitude of the charges on both the ends/point of the dipole
$\vec{E}$ = Electric field applied on the dipole
ϴ = Angle of rotation of dipole with its axis in presence of electric field
Complete answer:
On both the dipoles, the force will be
$\tau=+q\times\vec{E}\ sin\theta$ (anticlockwise for the one point of the dipole)
$\tau=-q\times\vec{E}\ sin\theta$ (clockwise for the other point of the dipole)
So, the torque acting on the dipole is
$\tau=q\times\vec{E}\ sin\theta$
Since; Since the values of sinϴ are-
As, Sin90˚= 1
So we can see that at an angle of 90˚ the dipole will experience the maximum torque because its value is 1 (maximum).
Thus, the value of torque will be maximum at an angle of 90˚
Note: Torque is a vector quantity it depends on the direction of the force. The distance between the point where force is applied and the point of rotation at the dipole is called an arm. One should know the concept of stable and unstable equilibrium also to understand the question.
Recently Updated Pages
JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

Young's Double Slit Experiment Step by Step Derivation

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

JEE Energetics Important Concepts and Tips for Exam Preparation

JEE Isolation, Preparation and Properties of Non-metals Important Concepts and Tips for Exam Preparation

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

Electric field due to uniformly charged sphere class 12 physics JEE_Main

Displacement-Time Graph and Velocity-Time Graph for JEE

Uniform Acceleration

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

JEE Advanced 2025: Dates, Registration, Syllabus, Eligibility Criteria and More

JEE Advanced Weightage 2025 Chapter-Wise for Physics, Maths and Chemistry

Degree of Dissociation and Its Formula With Solved Example for JEE

Free Radical Substitution Mechanism of Alkanes for JEE Main 2025

If a wire of resistance R is stretched to double of class 12 physics JEE_Main
