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 1.0 mn in diameter, evenly wound in a single layer to form a helical coil of 40 cm and diameter 12 cm . 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.

The solenoid is removed from the enclosure and then used in a location where the earth’s magnetic field is and points horizontally. A sample of bacteria is placed in the center of the solenoid, and the same current is applied that produced a magnetic field of $\mathbf{50}\mathit{\mu }\mathit{T}$ in the lab. Describe the field experienced

by the bacteria: The field (a) is still 150 mT; (b) is now 200$\mathit{\mu }\mathit{T}$ ; (c) is between 100 and 200 mT, depending on how the solenoid is oriented; (d) is between50and 150role="math" localid="1668272949634" $\mathit{\mu }\mathit{T}$, depending on how the solenoid is oriented.

Short answer

The correct option is (c).

Step-by-step solution

  Identification of the concept

The magnetic field due to a solenoid inside is,

$\mathit{B}\mathbf{=}{\mathit{\mu }}_{\mathbf{0}}\mathit{n}\mathit{l}$

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

Determination of the maximum torque in new solenoid.

The shielding effect provided by the enclosure is gone leaving the solenoid bare to earth’s magnetic field’s influence. Therefore, the resultant magnetic field is dependent on both the solenoid field and the earth field and the orientation of the solenoid decides whether the earth’s magnetic field adds or subtracts to it.

When the solenoid filed is parallel to earth’s field,

$\begin{array}{r}B=150\mu T+50\mu T\\ =200\mu T\end{array}$

When the solenoid filed is anti-parallel to earth’s field,

$\begin{array}{r}B=150\mu T-50\mu T\\ =200\mu T\end{array}$

Thus, the range of the magnetic field experienced by the bacteria is between 100µT to 200µT.