
Four wires, each of length 2 m, are bent into four loops P, Q, R and S and then suspended in uniform magnetic field. If the same current is passed in each, then in which loop will the torque be maximum?

A. P
B. Q
C. R
D. S
Answer
162k+ views
Hint: The given question is based on torque experienced on a current carrying loop placed in a uniform magnetic field or a magnetic dipole in a uniform magnetic field. The value of the torque is given by $\tau = iAB\sin \theta = MB\sin \theta $ , where $A$ is the area of the loop and $M$ is the magnetic dipole moment.
Complete answer:
Torque in a current carrying loop placed in a uniform magnetic field is given by:
$\tau = iAB\sin \theta $ … (1)
Where
$i$ is the current flowing through the loop,
$A$ is the area of the loop,
$B$ is the intensity of the magnetic field and
$\theta $ is the angle between the magnetic field and the axis of the loop.
For the given four loops, the only variable having a different value, to calculate the torque, is $A$ , that is, the area of the loop. It is given that each of the wires are of same length, 2m. For same perimeter, among the given figures, area of a circle will be maximum. Hence, when substituting all the values in (1), the value of the torque calculated will be maximum for the loop S, as its area is the most.
Thus, the correct option is D.
Note: In the above question, it is important to note that a circle is the most systematic shape for a given perimeter. Among all the shapes having the same perimeter, a circle is the one that will be having the maximum area.
Complete answer:
Torque in a current carrying loop placed in a uniform magnetic field is given by:
$\tau = iAB\sin \theta $ … (1)
Where
$i$ is the current flowing through the loop,
$A$ is the area of the loop,
$B$ is the intensity of the magnetic field and
$\theta $ is the angle between the magnetic field and the axis of the loop.
For the given four loops, the only variable having a different value, to calculate the torque, is $A$ , that is, the area of the loop. It is given that each of the wires are of same length, 2m. For same perimeter, among the given figures, area of a circle will be maximum. Hence, when substituting all the values in (1), the value of the torque calculated will be maximum for the loop S, as its area is the most.
Thus, the correct option is D.
Note: In the above question, it is important to note that a circle is the most systematic shape for a given perimeter. Among all the shapes having the same perimeter, a circle is the one that will be having the maximum area.
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
