A square loop with each side 1\,cm, carrying a current of 10\,A, is placed in a magnetic field of 0.2\,T. The direction of magnetic field is parallel to the plane of the loop. The torque experienced by the loop is . / 1\,cm प्रत्येक भुजा वाले एक वर्गाकार लूप को, जिसमें 10\,A की धारा प्रवाहित है, 0.2\,T के चुंबकीय क्षेत्र में रखा जाता है। चुंबकीय क्षेत्र की दिशा लूप के तल के समानांतर है। लूप पर लगने वाला बल-आघूर्ण (टॉर्क) होगा।

(2) 2 × 10^{-4}\,N·m Explanation (English): 1. Area of the square loop: A = a² = (1\,cm)² = (10⁻²\,m)² = 10^{-4}\,m² 2. Magnetic dipole moment of the loop: M = I A = 10\,A × 10^{-4}\,m² = 10⁻³\,A·m² 3. Torque on the magnetic dipole in a magnetic field {B}: {} = {M} × {B} = M B θ Here, the magnetic field {B} is parallel to the plane of the loop. The magnetic dipole moment {M} is directed along the normal to the plane of the loop. Therefore, the angle between {M} and {B} is θ = 90°: = (10⁻³\,A·m²)(0.2\,T) 90° = 2 × 10^{-4}\,N·m Hence, option 2 is the correct answer. व्याख्या (हिंदी): 1. वर्गाकार लूप का क्षेत्रफल: A = a² = (10⁻²\,m)² = 10^{-4}\,m² 2. चुंबकीय द्विध्रुव आघूर्ण: M = I A = 10 × 10^{-4} = 10⁻³\,A·m² 3. चुंबकीय क्षेत्र में लूप पर बल-आघूर्ण: = M B θ चूँकि चुंबकीय क्षेत्र लूप के तल के समानांतर है, अतः लूप के अभिलंब (द्विध्रुव आघूर्ण की दिशा) और {B} के मध्य कोण θ = 90° होगा: = 10⁻³ × 0.2 × 90° = 2 × 10^{-4}\,N·m अतः विकल्प 2 सही उत्तर है।

Q11: A square loop with each side $1\,\text{cm}$, carrying a current... - Magnetic Effects of Current and Magnetism - Physics CUET UG 16-05-2024 Shift 3 Set A Paper

Electrostatics Current Electricity Magnetic Effects of Current and Magnetism Electromagnetic Induction and Alternating Currents Electromagnetic Waves Optics Dual Nature of Matter and Radiation Atoms and Nuclei Electronic Devices

Physics CUET UG 16-05-2024 Shift 3 Set A Paper

MCQ (Single Correct) +5 −1

A square loop with each side $1\,\text{cm}$, carrying a current of $10\,\text{A}$, is placed in a magnetic field of $0.2\,\text{T}$. The direction of magnetic field is parallel to the plane of the loop. The torque experienced by the loop is _____.

$1\,\text{cm}$ प्रत्येक भुजा वाले एक वर्गाकार लूप को, जिसमें $10\,\text{A}$ की धारा प्रवाहित है, $0.2\,\text{T}$ के चुंबकीय क्षेत्र में रखा जाता है। चुंबकीय क्षेत्र की दिशा लूप के तल के समानांतर है। लूप पर लगने वाला बल-आघूर्ण (टॉर्क) ___________ होगा।

zero शून्य $2 \times 10^{-4}\,\text{N}\cdot\text{m}$ $2 \times 10^{-4}\,\text{N}\cdot\text{m}$ $2 \times 10^{-2}\,\text{N}\cdot\text{m}$ $2 \times 10^{-2}\,\text{N}\cdot\text{m}$ $2\,\text{N}\cdot\text{m}$ $2\,\text{N}\cdot\text{m}$

Area of the square loop:
$$A = a^2 = (1\,\text{cm})^2 = (10^{-2}\,\text{m})^2 = 10^{-4}\,\text{m}^2$$
Magnetic dipole moment of the loop:
$$M = I A = 10\,\text{A} \times 10^{-4}\,\text{m}^2 = 10^{-3}\,\text{A}\cdot\text{m}^2$$
Torque on the magnetic dipole in a magnetic field $\vec{B}$:
$$\vec{\tau} = \vec{M} \times \vec{B} \implies \tau = M B \sin\theta$$
Here, the magnetic field $\vec{B}$ is parallel to the plane of the loop. The magnetic dipole moment $\vec{M}$ is directed along the normal to the plane of the loop. Therefore, the angle between $\vec{M}$ and $\vec{B}$ is $\theta = 90^\circ$:
$$\tau = (10^{-3}\,\text{A}\cdot\text{m}^2)(0.2\,\text{T}) \sin 90^\circ = 2 \times 10^{-4}\,\text{N}\cdot\text{m}$$

Hence, option 2 is the correct answer.

वर्गाकार लूप का क्षेत्रफल:
$$A = a^2 = (10^{-2}\,\text{m})^2 = 10^{-4}\,\text{m}^2$$
चुंबकीय द्विध्रुव आघूर्ण:
$$M = I A = 10 \times 10^{-4} = 10^{-3}\,\text{A}\cdot\text{m}^2$$
चुंबकीय क्षेत्र में लूप पर बल-आघूर्ण:
$$\tau = M B \sin\theta$$
चूँकि चुंबकीय क्षेत्र लूप के तल के समानांतर है, अतः लूप के अभिलंब (द्विध्रुव आघूर्ण की दिशा) और $\vec{B}$ के मध्य कोण $\theta = 90^\circ$ होगा:
$$\tau = 10^{-3} \times 0.2 \times \sin 90^\circ = 2 \times 10^{-4}\,\text{N}\cdot\text{m}$$

अतः विकल्प 2 सही उत्तर है।

Explanation not matching this question? क्या व्याख्या इस प्रश्न से मेल नहीं खा रही? Report Mismatch त्रुटि बताएं

Electrostatics 8
Current Electricity 6
Magnetic Effects of Current and Magnetism 8
Electromagnetic Induction and Alternating Currents 7
Electromagnetic Waves 3
Optics 8
Dual Nature of Matter and Radiation 3
Atoms and Nuclei 4
Electronic Devices 3

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Q11: A square loop with each side $1\,\text{cm}$, carrying a current... - Magnetic Effects of Current and Magnetism - Physics CUET UG 16-05-2024 Shift 3 Set A Paper | Agrigyan

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