
A magnet of magnetic moment \[M\] is situated with its axis along the direction of a magnetic field of strength\[B\]. The work done in rotating it by an angle of \[{180^0}\] will be:
A. \[ - MB\]
B. \[ + MB\]
C. \[ + 2MB\]
D. \[Zero\]
Answer
161.4k+ views
Hint:
To solve this question we have to use the basic formula of work done in moving a dipole in an external magnetic field. Use the given data and by putting it into the equation we can directly solve the question.
Formula used:
\[W = MB(1 - \cos \theta )\]
\[M\]- magnetic moment of the dipole
\[B\]- magnetic field strength
Complete step by step solution:
let us solve the given question by using the given data.
Given data: \[M\]- magnetic moment of the dipole.
\[B\]- magnetic field strength
\[\theta = {180^0}\]
Now, by using formula for work done in moving the dipole with magnetic moment in given magnetic field by the angle of \[{180^0}\] we have:
\[W = MB(1 - \cos \theta )\]
By using \[\theta = {180^0}\]in above equation we get
\[ \Rightarrow W = MB(1 - \cos {180^0})\]
\[ \Rightarrow W = MB(1 - ( - 1))\]
\[ \Rightarrow W = 2MB\]
Hence, the work done on the magnet to rotate it with the angle of \[{180^0}\]is \[2MB\].
Correct answer is option c.
Therefore, the correct option is C.
Note:
In this question, the dipole is along the magnetic field also called stable equilibrium position and rotating the magnet by \[{180^0}\] then it will be at unstable equilibrium position. A particle always tries to remain at a stable equilibrium position so whenever we move the dipole from its stable equilibrium position we have to do some extra work.
To solve this question we have to use the basic formula of work done in moving a dipole in an external magnetic field. Use the given data and by putting it into the equation we can directly solve the question.
Formula used:
\[W = MB(1 - \cos \theta )\]
\[M\]- magnetic moment of the dipole
\[B\]- magnetic field strength
Complete step by step solution:
let us solve the given question by using the given data.
Given data: \[M\]- magnetic moment of the dipole.
\[B\]- magnetic field strength
\[\theta = {180^0}\]
Now, by using formula for work done in moving the dipole with magnetic moment in given magnetic field by the angle of \[{180^0}\] we have:
\[W = MB(1 - \cos \theta )\]
By using \[\theta = {180^0}\]in above equation we get
\[ \Rightarrow W = MB(1 - \cos {180^0})\]
\[ \Rightarrow W = MB(1 - ( - 1))\]
\[ \Rightarrow W = 2MB\]
Hence, the work done on the magnet to rotate it with the angle of \[{180^0}\]is \[2MB\].
Correct answer is option c.
Therefore, the correct option is C.
Note:
In this question, the dipole is along the magnetic field also called stable equilibrium position and rotating the magnet by \[{180^0}\] then it will be at unstable equilibrium position. A particle always tries to remain at a stable equilibrium position so whenever we move the dipole from its stable equilibrium position we have to do some extra work.
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

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

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

Formula for number of images formed by two plane mirrors class 12 physics JEE_Main

Uniform Acceleration

Degree of Dissociation and Its Formula With Solved Example for JEE
