Question

Some types of bacteria contain chains of ferromagnetic particles parallel to their long axis. The chains act like small bar magnets that align these magnetotactic bacteria with the earth’s magnetic field. In one experiment to study the response of such bacteria to magnetic fields, a solenoid is constructed with copper wire in diameter, evenly wound in a single layer to form a helical coil of and diameter . The wire has a very thin layer of insulation, and the coil is wound so that adjacent turns are just touching. The solenoid, which generates a magnetic field, is in an enclosure that shields it from other magnetic fields. A sample of magnetotactic bacteria is placed inside the solenoid. The torque on an individual bacterium in the solenoid’s magnetic field is proportional to the magnitude of the magnetic field and to the sine of the angle between the long axis of the bacterium and the magnetic-field direction.

To use a larger sample, the experimenters construct a solenoid that has the same length, type of wire, and loop spacing but twice the diameter of the original. How does the maximum possible magnetic torque on a bacterium in this new solenoid compare with the torque the bacterium would have experienced in the original solenoid? Assume that the currents in the solenoids are the same. The maximum torque in the new solenoid is (a) twice that in the original one; (b) half that in the original one; (c) the same as that in the original one; (d) one-quarter that in the original one.

Short answer

The correct option is (c).

Step-by-step solution

  Identification of the concept

$\mathbf{B}\mathbf{=}{\mathit{\mu }}_{\mathbf{0}}\mathit{n}\mathit{l}$The magnetic field due to a solenoid inside is,

Where, B is the magnetic field magnitude, n is the total number of turns or loops and l is the current flowing through the solenoid.

Determination of the maximum torque in the new solenoid.

According to the solenoid equation, the magnetic field inside a solenoid is dependent on the number of terms, the current, and also length. Since all three factors are the same in both the solenoids, thus, the magnetic field is also the same in the solenoids. Hence, option (c) is correct.