91影视

Some types of bacteria contain chains of ferromagnetic particles parallel to their long axis. The chains act like small bar magnets that align these

magnetotacticbacteria with the earth鈥檚 magnetic field. In one experiment to study the response of such bacteria to magnetic fields, a solenoid is constructed with copper wire 1.0 mm 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鈥檚 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.

What current is needed in the wire so that the magnetic field experienced by the bacteria has a magnitude of 150 mT? (a) 0.095 A; (b) 0.12 A; (c) 0.30 A; (d) 14 A.

Step by step solution

01

 Identification of the concept

The magnetic field due to a solenoid inside is,

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

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.

02

Determination of the magnitude of current needed.

Consider the ideal solenoid equation although the solenoid in this case is not ideal because of its length being way greater than its width.

Thus,

$\begin{array}{r}B={渭}_0\mathrm{nl}\\ ={渭}_0\left(1000{\mathrm{m}}^{鈭�1}\right)I\\ =150脳{10}^{鈭�6}\mathrm{T}\end{array}$

Solve for the current,

$\begin{array}{l}l=\frac{B}{{渭}_{0}n}\\ =0.12A\end{array}$

Thus, the magnitude of the current is 0.12 A.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!