Fish Magnetic Field Question

[Yosty22]

Homework Statement

Certain fish, such as the Nile fish (Gnathonemus), concentrate charges in their head and tail, thereby producing an electric field in the water around them. This field creates a potential difference of a few volts between the head and tail, which in turn causes current to flow in the conducting seawater. As the fish swims, it passes near objects that have resistivities different from that of seawater, which in turn causes the current to vary. Cells in the skin of the fish are sensitive to this current and can detect changes in it. The changes in the current allow the fish to navigate.Since the electric field is weak far from the fish, we shall consider only the field running directly from the head to the tail. We can model the seawater through which that field passes as a conducting tube of area and having a potential difference across its ends. These fish navigate by responding to changes in the current in seawater. This current is due to a potential difference of around 3.00V generated by the fish and is about 12.0mA within a centimeter or so from the fish. Receptor cells in the fish are sensitive to the current. Since the current is at some distance from the fish, their sensitivity suggests that these cells might be responding to the magnetic field created by the current. To get some estimate of how sensitive the cells are, we can model the current as that of a long, straight wire with the receptor cells 2.00cm away.

What is the strength of the magnetic field at the receptor cells?

Homework Equations

B=μ_0*I/(2*pi*r)

The Attempt at a Solution

Since you can think of this as a long, straight, current carryign conductor, I used the equation shown above. I made sure my units were correct, and I got B=1.2*10^-7T, which is wrong. This question is pretty weird. Any help would be much appreciated.

 

[anathema]

Hello, thank you for your question. I would like to offer some insights and suggestions for solving this problem.

Firstly, it is important to understand the concept of the magnetic field and how it is related to current and distance. The magnetic field strength is directly proportional to the current and inversely proportional to the distance. This means that as the current increases, the magnetic field strength also increases, and as the distance increases, the magnetic field strength decreases.

In this problem, we are given the current (12.0mA) and the distance (2.00cm) from the fish. Therefore, we can use the equation B=μ_0*I/(2*pi*r) to calculate the magnetic field strength at the receptor cells.

However, the key here is to determine the value of μ_0, which is the permeability of free space. This value is a constant and is equal to 4πx10^-7 T*m/A. By substituting the given values into the equation, we get B=1.2x10^-7 T, which is the correct answer.

It is important to note that the sensitivity of the receptor cells does not affect the calculation of the magnetic field strength. The sensitivity only determines the ability of the cells to detect changes in the magnetic field.

I hope this helps to clarify the problem and provides some guidance for solving it. Remember, as a scientist, it is important to understand the concepts and equations and use them correctly to arrive at the correct solution. Keep up the good work!