B

The torque \( \tau \) acting on a rectangular coil in a magnetic field can be expressed as:
\( \tau = n \cdot B \cdot I \cdot A \cdot \sin \theta \)
where
- \( n \) is the number of turns,
- \( B \) is the magnetic field strength,
- \( I \) is the current through the coil,
- \( A \) is the area of the coil,
- \( \theta \) is the angle between the magnetic field and the normal to the coil's surface.
To double the torque, we may either double the area \( A \), double the current \( I \), or any combination that leads to a product that is doubled. Therefore, the most straightforward methods to achieve this are given by option B: area or current through the coil should be doubled.