Torque on a Current Loop MCQ Quiz in বাংলা - Objective Question with Answer for Torque on a Current Loop - বিনামূল্যে ডাউনলোড করুন [PDF]

CONCEPT:

• When a magnetic dipole of moment \(\vec M\) is held at an angle θ with the direction of a uniform magnetic field \(\vec B\), then it experiences a torque.

The magnitude of the torque acting on the dipole is

τ = M B sin θ

Where M is magnetic moment and B is magnetic field

CALCULATION:

Given – Number of turns (N) = 10, I = 10 A, B = 5 T and radius (r) = 7 cm = 7 × 10^-2 m

θ = 30°

The magnitude of the torque acting on the circular coil is:

τ = M B sin θ

Here, M = INA

\(\Rightarrow M = 10 \times 10 \times \frac{{22}}{7} \times {\left( {7 \times {{10}^{ - 2}}} \right)^2}\)

⇒ M = 154 × 10^-2 Am²

⇒ τ = 154 × 10^-2 × 5 × sin 30°

⇒ τ = 385 × 10^-2 Nm

So option 2 is correct.

CONCEPT:

• As the current-carrying conductor experiences a force when placed in a magnetic field, each side of a current-carrying circular coil experiences a force in a magnetic field.
•  In the present section, we shall see in what way the circular loop carrying current is influenced by a magnetic field.

• Consider a circular coil of length l and breadth b carrying a current I placed in a uniform magnetic field B.
• θ, be the angle between the plane of the circular coil and the magnetic field.

 Force acting on the circular loop:

F = I L B sinθ, where F is force, I = current, L = distance from the axis, B = strength of the magnetic field, θ = angle between the plane of the circular coil and the magnetic field.

• Acting on the upper and lower sides are equal and opposite along the same line of action, they cancel each other.
• As the force acting on the sides QR and SP are equal and opposite along different lines of action they constitute a couple.

So, the torque acting on the loop is,

T = force × arm of the couple

T = B I L × b Sinθ = B I A Sinθ

T = B I A Sinθ

EXPLANATION:

• The torque acting on a circular current-carrying loop placed in a uniform magnetic field depends upon
  • area of the loop
  • value of current
  • magnetic field
• The torque acting on the circular loop is

T = B I A Sinθ.

• Therefore option 1 is incorrect.

CONCEPT:

• As the current-carrying conductor experiences a force when placed in a magnetic field, each side of a current-carrying rectangular coil experiences a force in a magnetic field.
•  In the present section, we shall see in what way the rectangular loop carrying current is influenced by a magnetic field.

• Consider a rectangular coil of length l and breadth b carrying a current I placed in a uniform magnetic field B.
• θ, be the angle between the plane of the rectangular coil and the magnetic field.

Force acting on the rectangular loop:

F = I L B sinθ, where F is force, I = current, L = distance from the axis, B = strength of the magnetic field, θ = angle between the plane of the rectangular coil and the magnetic field.

• Acting on the upper and lower sides are equal and opposite along the same line of action, they cancel each other.
• As the force acting on the sides QR and SP are equal and opposite along different lines of action they constitute a couple.

So, the torque acting on the loop is,

T = force × arm of the couple

T = B I L × b Sinθ = B I A Sinθ

T = B I A Sinθ

EXPLANATION:

• The torque acting on the rectangular loop is

T = B I A sin θ.

So option 2 is correct.

The correct answer is: 1) Magnetic field

Explanation:

The magnetic field is the region around a magnet (or current-carrying conductor) where its magnetic force influences other magnets, magnetic materials, or moving charges. It is represented by field lines that show the direction and strength of the force.

Option Analysis

2. Magnetic flux → Refers to the total number of magnetic field lines passing through a surface (measured in Weber).

3. Magnetic domain → Microscopic regions within a material where atomic magnetic moments are aligned.

4. Magnetic pole → The points (north/south) on a magnet where the magnetic field is strongest, not the surrounding region.

Additional Information

• Magnetic fields are vector fields (have direction and magnitude).

• They extend infinitely but weaken with distance.

• Field lines never cross and always form closed loops.

CONCEPT:

Torque on a rectangular current loop in a uniform magnetic field:

• If a rectangular loop carrying a steady current is placed in a uniform magnetic field then it will experience a torque.
  • The net force on the loop will be zero.
• The torque on the current-carrying rectangular loop is given as,

⇒ τ = NIAB.sinθ

Where N = number of turns in the coil, I = current in the loop, A = area enclosed by the loop, B = magnetic field intensity, and θ = angle between the normal to the plane of the coil and the direction of a uniform magnetic field

• The magnetic moment m for the loop is given as,

⇒ m = NIA

So,

\(⇒ τ = mBsinθ = \vec{m}×\vec{B}\)

CALCULATION:

Given L = 40 cm = 0.4 m, W = 10 cm = 0.1 m, N = 10 turns, I = 16 A, θ = 60°, and B = 0.60 T

Where N = number of turns in the coil, I = current in the loop, A = area enclosed by the loop, L = length of the loop, W = width of the loop, B = magnetic field intensity, and θ = angle between the normal to the plane of the coil and the direction of a uniform magnetic field

• The area enclosed by the loop is given as,

⇒ A = L × W

⇒ A = 0.4 × 0.1

⇒ A = 0.04 m²

• So the torque on the current-carrying rectangular loop is given as,

⇒ τ = IAB sinθ

⇒ τ = 16 × 0.04 × 0.6 × sin60

\(\Rightarrow τ=\frac{16\times4\times6\times\sqrt3}{10\times10\times2}\)

\(⇒ τ = 1.92\sqrt3\, N-m\)

• Hence, option 2 is correct.

CONCEPT:

Torque on a rectangular current loop in a uniform magnetic field:

• If a rectangular loop carrying a steady current is placed in a uniform magnetic field then it will experience a torque.
  • The net force on the loop will be zero.
• The torque on the current-carrying rectangular loop is given as,

⇒ τ = NIAB.sinθ

Where N = number of turns in the coil, I = current in the loop, A = area enclosed by the loop, B = magnetic field intensity, and θ = angle between the normal to the plane of the coil and the direction of a uniform magnetic field

• The magnetic moment m for the loop is given as,

⇒ m = NIA

So,

\(⇒ τ = mB\,sinθ = \vec{m}\times\vec{B}\)

EXPLANATION:

• We know that the magnetic moment 'm' of the current-carrying loop is given as,

⇒ m = NIA

• Hence, option 1 is correct.

The correct answer is current through the coil is increased.

Key Points

• The magnetic field around a current-carrying coil is directly proportional to the current passing through the coil.
• Increasing the current results in a stronger magnetic field as per Ampere's Law, which states that the magnetic field is proportional to the current.
• The strength of the magnetic field can be calculated using the formula B = μ₀ * (n * I), where B is the magnetic field, μ₀ is the permeability of free space, n is the number of turns, and I is the current.
• This relationship is fundamental in electromagnetism and is utilized in various applications such as electromagnets, transformers, and inductors.

Additional Information

• Ampere's Law:
  • Ampere's Law relates the circulating magnetic field in a closed loop to the electric current passing through the loop.
  • The mathematical expression of Ampere's Law is ∮B·dl = μ₀ * I, where B is the magnetic field, dl is an infinitesimal element of the path, and I is the current enclosed by the path.
• Electromagnetism:
  • Electromagnetism is the branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles.
  • It is the fundamental principle behind electric motors, transformers, and many other modern devices.
• Magnetic Field Strength:
  • Magnetic field strength, often denoted as H, is a measure of the magnetizing force and is directly proportional to the current and inversely proportional to the distance from the current-carrying conductor.
• Permeability of Free Space (μ₀):
  • Permeability of free space, also known as the magnetic constant, is a physical constant that describes the magnetic permeability in a classical vacuum.
  • Its value is approximately 4π × 10⁻⁷ H/m (henries per meter).

CONCEPT:

Torque on a rectangular current loop in a uniform magnetic field:

• If a rectangular loop carrying a steady current is placed in a uniform magnetic field then it will experience a torque.
  • The net force on the loop will be zero.
• The torque on the current-carrying rectangular loop is given as,

⇒ τ = NIAB.sinθ

Where N = number of turns in the coil, I = current in the loop, A = area enclosed by the loop, B = magnetic field intensity, and θ = angle between the normal to the plane of the coil and the direction of a uniform magnetic field

• The magnetic moment m for the loop is given as,

⇒ m = NIA

So,

\(⇒ τ = mB.sinθ = \vec{m}\times\vec{B}\)

EXPLANATION:

• If a rectangular loop carrying a steady current is placed in a uniform magnetic field then it will experience a torque.
• The net force on the loop will be zero. Hence, option 2 is correct.

CONCEPT:

Torque on a rectangular current loop in a uniform magnetic field:

• If a rectangular loop carrying a steady current is placed in a uniform magnetic field then it will experience a torque.
  • The net force on the loop will be zero.
• The torque on the current-carrying rectangular loop is given as,

⇒ τ = NIAB.sinθ

Where N = number of turns in the coil, I = current in the loop, A = area enclosed by the loop, B = magnetic field intensity, and θ = angle between the normal to the plane of the coil and the direction of a uniform magnetic field

• The magnetic moment m for the loop is given as,

⇒ m = NIA

So,

\(⇒ τ = mB.sinθ = \vec{m}\times\vec{B}\)

EXPLANATION:

Given I = current in the loop, A = area enclosed by the loop, B = magnetic field intensity, and θ = angle between the magnetic field and the area

• So the torque on the current-carrying rectangular loop is given as,

⇒ τ = IAB.sinθ

• Hence, option 1 is correct.

CONCEPT:

Voltammeter:

• A voltammeter or coulometer is a scientific instrument used for measuring the quantity of electricity (electric charge) through electrolytic action.
  • The SI unit of quantity of electricity is the coulomb.

Voltmeter:

• A voltmeter is an instrument used for measuring the electric potential difference between two points in an electric circuit.
  • Analog voltmeters move a pointer across a scale in proportion to the voltage of the circuit; digital voltmeters give a numerical display of voltage by use of an analog-to-digital converter

Galvanometer: 

• A galvanometer works on the principle When a current-carrying coil is placed in an external magnetic field a magnetic torque is acting on it, and which is given by 

⇒ τ = NABI Sinθ 

Where N = Number of turns B = Magnetic field I = Current A = Area

EXPLANATION:

• ​According to the principle of the galvanometer, the angle through which the loop is rotated is proportional to the current in the coil i.e.,

⇒ θ ∝ I 

• Hence, option 3 is the answer