Question

Torque acting on a coil carrying current 'I' situated parallel to magnetic field of induction 'B' having of turns 'n' and area 'A' is

• A. \(\text{nI}(\overset{⃗}{A}\cdot \overset{⃗}{B})\)
• B. \(\text{nI}(\overset{⃗}{A}\times \overset{⃗}{B})\)
• C. \(\text{IBA}/\text{n}\)
• D. \(\text{nBA}/\text{I}\)

Hint:

Torque on a coil is n I A cross B.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
A coil with \(n\) turns, current \(I\) and area vector \(\vec A\) has magnetic moment \(\vec m = nI\vec A\).

Step 2: Torque:
\[ \vec\tau = \vec m\times\vec B = nI(\vec A\times\vec B) \]
When the coil plane is parallel to the field, \(\vec A\) is perpendicular to \(\vec B\), so the magnitude is \(nIAB\), the maximum torque.

Step 3: Check the options:
Option (B) is the vector form. Option (A) uses a dot product, which would give zero here. Options (C) and (D) divide by \(n\) or \(I\), which does not agree with torque being proportional to both.

Final Answer:
Torque is n I (A cross B). \[ \boxed{\text{(B) }nI(\vec A\times\vec B)} \]