Question

A rectangular coil of \(n\) turns has area \(\vec{A}\) and it is placed in uniform magnetic field \(\vec{B}\). If the current passing through the coil is 'I' then the torque acting on the coil is

• A. \(\frac{I}{n}(\vec{A}\times \vec{B})\)
• B. \(nI(\vec{A}\cdot \vec{B})\)
• C. \(nI(\vec{A}\times \vec{B})\)
• D. \(\frac{n}{I}(\vec{A}\cdot \vec{B})\)

Hint:

Torque is the cross product of the magnetic moment and the field.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
Magnetic moment of the coil is \(\vec{M}=nI\vec{A}\).

Step 2: Torque
\(\vec{\tau}=\vec{M}\times\vec{B}\).

Step 3: Result
\(\vec{\tau}=nI(\vec{A}\times\vec{B})\).

Final Answer:
The torque on the coil is nI times A cross B. \[ \boxed{\text{(C) }nI(\vec{A}\times\vec{B})} \]