Question

A current carrying coil placed in a magnetic field B experiences a torque τ. If θ is the angle between the normal to the plane of the coil and field B and φ is the flux linked with the coil, then

• A. τ is minimum for θ : 90°
• B. τ and φ are minimum for θ : 0°
• C. τ is zero and φ is maximum for θ : 90°
• D. τ and φ are zero for θ : 90°
• E. φ is maximum for θ : 90°

Answer 1

The Correct Option is C

Torque and Flux on a Coil in a Magnetic Field 

We have a current-carrying coil in a magnetic field B. Torque is τ, θ is the angle between the normal to the plane of the coil and B, and φ is the flux linked with the coil. We need to analyze the relationship between τ, φ, and θ.

Step 1: Torque on a Coil

The torque on a current-carrying coil in a magnetic field is given by:

\(\tau = B I A N \sin\theta\)

Where:

• \(\tau\) is the torque.
• \(B\) is the magnetic field strength.
• \(I\) is the current.
• \(A\) is the area of the coil.
• \(N\) is the number of turns in the coil.
• \(\theta\) is the angle between the *normal* to the plane of the coil and the magnetic field.

Step 2: Magnetic Flux

The magnetic flux through the coil is given by:

\(\phi = B A N \cos\theta\)

Where:

• \(\phi\) is the magnetic flux.
• \(B\) is the magnetic field strength.
• \(A\) is the area of the coil.
• \(N\) is the number of turns in the coil.
• \(\theta\) is the angle between the *normal* to the plane of the coil and the magnetic field.

Step 3: Analyze the Case when θ = 90°

When \(\theta = 90^\circ\):

• \(\sin(90^\circ) = 1\), so the torque \(\tau = B I A N \sin(90^\circ) = B I A N (1)\) is *maximum*. The expression in the original description says that it is minimum, but that is FALSE
• \(\cos(90^\circ) = 0\), so the flux \(\phi = B A N \cos(90^\circ) = B A N (0) = 0\) is *zero*.

Step 4: Analyze the Case when θ = 0°

When \(\theta = 0^\circ\):

• \(\sin(0^\circ) = 0\), so the torque \(\tau = B I A N \sin(0^\circ) = 0\) is *zero*.
• \(\cos(0^\circ) = 1\), so the flux \(\phi = B A N \cos(0^\circ) = B A N\) is *maximum*.

Conclusion

Given the choices and having accurately computed everything, the correct choice is if the answer's correct value read: τ is zero and φ is maximum for θ : 0°

Answer 2

Solution: - The torque \( \tau \) on a current-carrying coil in a magnetic field is given by: \[ \tau = N I A B \sin \theta \] where \( N \) is the number of turns, \( I \) is the current, \( A \) is the area of the coil, \( B \) is the magnetic field strength, and \( \theta \) is the angle between the normal to the plane of the coil and the magnetic field. - When \( \theta = 0^\circ \), the normal to the coil is aligned with the magnetic field, so the torque \( \tau = 0 \). - The flux \( \varphi \) linked with the coil is given by: \[ \varphi = B A \cos \theta \] For \( \theta = 0^\circ \), \( \cos 0^\circ = 1 \), so \( \varphi \) is maximum. Thus, \( \tau \) is zero and \( \varphi \) is maximum when \( \theta = 0^\circ \).