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: Force on sides:
Each of the two long sides carries force $nIlB$ in opposite directions, separated by the width $b$.

Step 2: Couple:
Torque $= nIlB\,b = nIAB$ for a coil parallel to the field.

Step 3: Vector form:
This is the magnitude of $nI(\vec A\times\vec B)$, option (B).

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