Question

A rectangular coil of 400 turns and \(10^{-2} \, \text{m}^2\) area, carrying a current of 0.5 A is placed in a uniform magnetic field of 1 T such that the plane of the coil makes an angle of 60° with the direction of the magnetic field. The initial moment of force acting on the coil in Nm is:

• A. \( \sqrt{3} \)
• B. \( \frac{1}{\sqrt{3}} \)
• C. 1
• D. \( \frac{\sqrt{3}}{2} \)

Hint:

The torque on a coil in a magnetic field is maximum when the plane of the coil is perpendicular to the magnetic field and minimum when the plane is parallel to the field.

Answer 1

The Correct Option is C

We are tasked with finding the initial moment of force (torque) acting on a rectangular coil placed in a uniform magnetic field. The given parameters are: Number of turns, \(N = 400\),
Area of the coil, \(A = 10^{-2} \, \text{m}^2\),
Current through the coil, \(I = 0.5 \, \text{A}\),
Magnetic field strength, \(B = 1 \, \text{T}\),
Angle between the plane of the coil and the magnetic field, \(\theta = 60^\circ\). Step 1: Recall the formula for torque on a current-carrying coil The torque (\(\tau\)) acting on a current-carrying coil in a magnetic field is given by: \[ \tau = N \cdot I \cdot A \cdot B \cdot \sin(\phi) \] where:
\(N\) is the number of turns,
\(I\) is the current,
\(A\) is the area of the coil,
\(B\) is the magnetic field strength,
\(\phi\) is the angle between the magnetic field and the normal to the plane of the coil.
Step 2: Determine the angle \(\phi\) The angle \(\theta = 60^\circ\) is the angle between the plane of the coil and the magnetic field. The angle \(\phi\) is the angle between the normal to the plane of the coil and the magnetic field. These two angles are complementary, so: \[ \phi = 90^\circ - \theta = 90^\circ - 60^\circ = 30^\circ \] Step 3: Substitute values into the torque formula Substitute the given values into the torque formula: \[ \tau = N \cdot I \cdot A \cdot B \cdot \sin(\phi) \] \[ \tau = 400 \cdot 0.5 \cdot 10^{-2} \cdot 1 \cdot \sin(30^\circ) \] Simplify: \[ \tau = 400 \cdot 0.5 \cdot 10^{-2} \cdot 1 \cdot 0.5 \] \[ \tau = 400 \cdot 0.5 \cdot 10^{-2} \cdot 0.5 \] \[ \tau = 400 \cdot 0.0025 \] \[ \tau = 1 \, \text{Nm} \] Thus, the initial moment of force acting on the coil is 1 Nm.