Question:
A rectangular coil of length 2 cm and width 1.25 cm with 250 turns carries a current of 55 μA and is subjected to a magnetic field of strength 0.64 T. Work done in rotating the coil by 180° against the torque is:
A rectangular coil of length 2 cm and width 1.25 cm with 250 turns carries a current of 55 μA and is subjected to a magnetic field of strength 0.64 T. Work done in rotating the coil by 180° against the torque is:
Show Hint
For a coil in magnetic field, full rotation work depends only on change in potential energy: \(W = 2mB\).
Updated On: Jun 20, 2026
- 2.2 μJ
- 3.5 μJ
- 4.4 μJ
- 5.5 μJ
Show Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Concept of magnetic dipole work.
A current-carrying coil behaves like a magnetic dipole having magnetic moment: \[ m = N I A \] Work done in rotating a dipole from \(0^\circ\) to \(180^\circ\) is: \[ W = 2mB \]
Step 2: Convert area into SI units.
\[ A = 2 \times 1.25 = 2.5 \, \text{cm}^2 = 2.5 \times 10^{-4} \, \text{m}^2 \]
Step 3: Calculate magnetic moment.
\[ m = 250 \times 55 \times 10^{-6} \times 2.5 \times 10^{-4} \]
Step 4: Simplify step-by-step.
First multiply current and area: \[ 55 \times 10^{-6} \times 2.5 \times 10^{-4} = 137.5 \times 10^{-10} = 1.375 \times 10^{-8} \] Now multiply by turns: \[ m = 250 \times 1.375 \times 10^{-8} = 3.4375 \times 10^{-6} \, \text{A m}^2 \]
Step 5: Work done for 180° rotation.
\[ W = 2mB \] \[ W = 2 \times 3.4375 \times 10^{-6} \times 0.64 \] \[ W = 4.4 \times 10^{-6} \, \text{J} \]
Step 6: Final interpretation.
\[ \boxed{4.4 \, \mu \text{J}} \]
A current-carrying coil behaves like a magnetic dipole having magnetic moment: \[ m = N I A \] Work done in rotating a dipole from \(0^\circ\) to \(180^\circ\) is: \[ W = 2mB \]
Step 2: Convert area into SI units.
\[ A = 2 \times 1.25 = 2.5 \, \text{cm}^2 = 2.5 \times 10^{-4} \, \text{m}^2 \]
Step 3: Calculate magnetic moment.
\[ m = 250 \times 55 \times 10^{-6} \times 2.5 \times 10^{-4} \]
Step 4: Simplify step-by-step.
First multiply current and area: \[ 55 \times 10^{-6} \times 2.5 \times 10^{-4} = 137.5 \times 10^{-10} = 1.375 \times 10^{-8} \] Now multiply by turns: \[ m = 250 \times 1.375 \times 10^{-8} = 3.4375 \times 10^{-6} \, \text{A m}^2 \]
Step 5: Work done for 180° rotation.
\[ W = 2mB \] \[ W = 2 \times 3.4375 \times 10^{-6} \times 0.64 \] \[ W = 4.4 \times 10^{-6} \, \text{J} \]
Step 6: Final interpretation.
\[ \boxed{4.4 \, \mu \text{J}} \]
Was this answer helpful?
0
0
Top AP EAPCET Physics Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The radii of the two columns in a U - tube are r1 and r2. When a liquid of density p (angle of contact is $ 0{}^\circ $ ) is filled in it, the level difference of the liquid in the two arms is h. The surface tension of the liquid is: (g = acceleration due to gravity)
- A rigid metallic sphere is spinning around its own axis in the absence of external torque. If the temperature is raised, its volume increases by $9 \%$. The change in its angular speed is
View More Questions
Top AP EAPCET Magnetic Field Questions
- In a hydrogen atom, an electron is making \( 6.6 \times 10^5 \) revolutions around the nucleus of radius \( 0.47 \) Å. The magnetic field induction produced at the center of the orbit is nearly:
- Any magnetic material loses its magnetic property when it is:
- The magnitude of the magnetic field due to a circular coil of radius R carrying a current I at its centre is
- The properties of a material required to make permanent magnets are
A straight conductor carries a current of 10 A. The magnetic field at a distance of 2 cm from the wire is: (μ₀ = 4 × 10⁻⁷ T m/A)
View More Questions
Top AP EAPCET Questions
- A body is projected from the ground at an angle of $\tan^{-1} \left( \frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is
- The four quantum numbers of the valence electron of potassium are :
- A lens forms real and virtual images of an object, when the object is at $u_{1}$ and $u_{2}$ distances respectively. If the size of the virtual image is double that of the real image, then the focal length of the lens is (take, the magnification of the real image as $m$ )
- Two spheres $P$ and $Q$, each of mass $200\, g$ are attached to a string of length one metre as shown in the figure. The string and the spheres are then whirled in a horizontal circle about $O$ at a constant angular speed. The ratio of the tension in the string between $P$ and $Q$ to that of between $P$ and $O$ is $(P$ is at mid-point of the line joining $O$ and $Q$ )
- The volume of $0.02\, M$ acidified permanganate solution required for complete reaction of $60\, mL$ of $0.01\, MI^{-}$ ion solution to form $I_2$ in $mL$ is
View More Questions