Question:
A circular coil of 100 turns has an effective radius of 0.05 m and carries a current of 0.1 A. How much work is required to turn it in an external magnetic field of 1.5 Wb/m\(^2\) through 180° about its axis perpendicular to the magnetic field? The plane of the coil is initially perpendicular to the magnetic field.
A circular coil of 100 turns has an effective radius of 0.05 m and carries a current of 0.1 A. How much work is required to turn it in an external magnetic field of 1.5 Wb/m\(^2\) through 180° about its axis perpendicular to the magnetic field? The plane of the coil is initially perpendicular to the magnetic field.
Show Hint
When the coil plane is initially perpendicular to \(B\), the normal is along \(B\) (minimum energy). Rotating 180° brings it to maximum energy: \(W = 2NiAB\).
Updated On: Apr 20, 2026
- 0.456 J
- 2.65 J
- 0.2355 J
- 3.95 J
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
Work done in rotating a magnetic dipole: \(W = U_f - U_i = -MB\cos\theta_f - (-MB\cos\theta_i)\).
Step 2: Detailed Explanation:
Initially, plane is perpendicular to \(B\) \(\Rightarrow\) axis parallel to \(B\): \(\theta_i = 0^\circ\). After rotation: \(\theta_f = 180^\circ\). Work done: \(W = 2NiAB\). Substitute values: \[ W = 2 \times 100 \times 0.1 \times (\pi \times 0.05^2) \times 1.5 = 2 \times 100 \times 0.1 \times 7.85\times10^{-3} \times 1.5 = 0.2355 \text{ J} \]
Step 3: Final Answer:
\[ \boxed{0.2355 \text{ J}} \]
Work done in rotating a magnetic dipole: \(W = U_f - U_i = -MB\cos\theta_f - (-MB\cos\theta_i)\).
Step 2: Detailed Explanation:
Initially, plane is perpendicular to \(B\) \(\Rightarrow\) axis parallel to \(B\): \(\theta_i = 0^\circ\). After rotation: \(\theta_f = 180^\circ\). Work done: \(W = 2NiAB\). Substitute values: \[ W = 2 \times 100 \times 0.1 \times (\pi \times 0.05^2) \times 1.5 = 2 \times 100 \times 0.1 \times 7.85\times10^{-3} \times 1.5 = 0.2355 \text{ J} \]
Step 3: Final Answer:
\[ \boxed{0.2355 \text{ J}} \]
Was this answer helpful?
0
0
Top MET Physics Questions
- A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- In intrinsic semiconductor at room temperature number of electrons and holes are
- A rope of mass $0.1\, kg$ is connected at the same height of two opposite walls. It is allowed to hang under its own weight. At [he contact point between the rope and the wall, the rope makes an angle $ \theta =10^{\circ} $ with respect to horizontal. The tension in the rope at its midpoint between the walls is
- At great distances from an electric dipole, the electric field strength due to the dipole varies with the distance as
View More Questions
Top MET Moving charges and magnetism Questions
Top MET Questions
- A coil of 100 turns and area $2 \times 10^{-2}m^2 $ is pivoted about a vertical diameter in a uniform magnetic field and carries a current of 5A. When the coil is held with its plane in north-south direction, it experiences a couple of 0.33 Nm. When the plane is east-west, the corresponding couple is 0.4 Nm, the value of magnetic induction is [Neglect earth's magnetic field]
- $\int\limits_{0}^{8}| x -5| d x$ is equal to
- Radiation, with wavelength 6561 $?$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3 \times 10^{-4} T$. If the radius of the largest circular path followed by the electrons is 10 mm, the work function of the metal is close to :
- In intrinsic semiconductor at room temperature number of electrons and holes are
- Which of the following product is formed in the reaction $ CH_3MgBr {->[(i)CO_2][(ii)H_2O]} ? $
View More Questions