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Chapter 28: Problem 19

BIO Currents in the Heart. The body contains many small currents caused by the motion of ions in the organs and cells. Measurements of the magnetic field around the chest due to currents in the heart give values of about 10\(\mu \mathrm{G}\) . Although the actual currents are rather complicated, we can gain a rough understanding of their magnitude if we model them as a long, straight wire. If the surface of the chest is 5.0 \(\mathrm{cm}\) from this current, how large is the current in the heart?

Short Answer

Expert verified
The current in the heart is approximately 0.5 A.

Step by step solution

01

Understanding the Problem

We are asked to find the current in the heart, modeled as a straight wire, given that the magnetic field at the chest's surface 5 cm away is 10 \(\mu \mathrm{G}\).
02

Magnetic Field Due to a Straight Wire

The magnetic field \(B\) at a distance \(r\) from a long, straight wire carrying current \(I\) is given by: \[ B = \frac{\mu_0 I}{2\pi r} \] where \(\mu_0\) is the permeability of free space (\(4\pi \times 10^{-7}\, \mathrm{T\,m/A}\)).
03

Rearranging the Formula

We need to solve for the current \(I\). Rearrange the formula to get: \[ I = \frac{2\pi r B}{\mu_0} \]
04

Substituting Given Values

Substitute the given values into the equation. Convert \(B = 10\, \mu \mathrm{G}\) to teslas and \(r = 5.0\, \mathrm{cm}\) to meters: \[ B = 10 \times 10^{-6}\, \mathrm{G} = 10 \times 10^{-10}\, \mathrm{T} \] \[ r = 5.0\, \mathrm{cm} = 0.05\, \mathrm{m} \]
05

Calculating the Current

Plug the values into the formula: \[ I = \frac{2\pi \times 0.05 \times 10 \times 10^{-10}}{4\pi \times 10^{-7}} \] Simplify to find \(I\): \[ I = \frac{1 \times 10^{-10}}{2 \times 10^{-7}} = 0.5 \] The current \(I\) is approximately 0.5 A.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Biophysics
Biophysics is the fascinating field that merges principles of biology and physics. It helps us understand how physical laws govern biological processes. In our specific exercise, biophysics plays a crucial role in analyzing how electric currents in the heart produce magnetic fields.
By modeling the currents in the heart as a straight wire, we use biophysical principles to solve for an unknown current. This can be simplified using mathematical equations derived from physics, thus providing insights into complex biological phenomena.
Biophysics is applied across various areas like neuroscience, molecular biology, and cardiac studies such as our example, where it links tiny ionic movements to a measurable output like the magnetic field near the heart. This interdisciplinary approach is key to deciphering how biological organisms function on a molecular and macro scale.
Magnetic Field
A magnetic field is invisible but influential. It surrounds magnets and electric currents, exerting forces on other nearby magnets and currents. In the body, these fields emerge from electrical activity, such as the tiny but significant currents of the heart.
The exercise refers to measuring the magnetic field around the chest due to heart currents, estimated at about 10 碌G. To understand this, we use the formula for the magnetic field generated by a long, straight current-carrying wire.
This field's strength decreases with distance from the source. Hence, knowing the magnetic field's value and distance from the wire allows us to determine the current's magnitude, offering a peek into the heart's electrical activity.
Cardiac Currents
Cardiac currents represent the flow of ions across heart cells, generating the electrical signals needed for heartbeats. These currents are crucial in keeping the heart rhythm steady and strong.
Electrodes can measure the signals directly, while magnetometers detect the magnetic fields they produce. In our example, modeling these currents as a wire simplifies the heart's complex electrical activity into a solvable model.
This analogy lets us apply physics equations to estimate the current strength based on its magnetic field. Cardiac currents are integral to the heart's function, and understanding them can aid in diagnosing and treating heart conditions.
Ion Motion in Biological Tissues
Ions are charged particles crucial for different biological processes, including nerve transmission and muscle contraction. In biological tissues, such as heart muscle, ions like sodium, potassium, and calcium flow in and out of cells.
This movement creates electrical currents essential for cellular communication and function. The ions' flow can be modeled like currents in a wire, as seen in the exercise where the heart's electrical activity is represented by a "current" producing a magnetic field.
Understanding ion motion helps in fields like electrophysiology, offering insights into how tissues like the heart or nerves transmit signals and maintain functions, crucial for life.

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Most popular questions from this chapter

A long, straight wire carries a current of 5.20 A. An electron is traveling in the vicinity of the wire. At the instant when the electron is 4.50 \(\mathrm{cm}\) from the wire and traveling with a speed of \(6.00 \times 10^{4} \mathrm{m} / \mathrm{s}\) directly toward the wire, what are the magnitude and direction (relative to the direction of the current) of the force that the magnetic field of the current exerts on the electron?

A \(+6.00-\mu \mathrm{C}\) point charge is moving at a constant \(8.00 \times 10^{6} \mathrm{m} / \mathrm{s}\) in the \(+y\) -direction, relative to a reference frame. At the instant when the point charge is at the origin of this reference frame, what is the magnetic-field vector \(\vec{B}\) it produces at the following points: (a) \(x=0.500 \mathrm{m}, y=0, \quad z=0 ;\) (b) \(x=0\) \(y=-0.500 \mathrm{m}, z=0 ; \quad(\mathrm{c}) x=0, \quad y=0, z=+0.500 \mathrm{m} ;\) (d) \(x=0, y=-0.500 \mathrm{m}, z=+0.500 \mathrm{m} ?\)

BIO Currents in the Brain. The magnetic field around the head has been measured to be approximately \(3.0 \times 10^{-8}\) G. Although the currents that cause this field are quite complicated, we can get a rough estimate of their size by modeling them as a single circular current loop 16 \(\mathrm{cm}\) (the width of a typical head) in diameter. What is the current needed to produce such a field at the center of the loop?

A toroidal solenoid with 500 turns is wound on a ring with a mean radius of 2.90 \(\mathrm{cm} .\) Find the current in the winding that is required to set up a magnetic field of 0.350 T in the ring (a) if the ring is made of annealed iron \(\left(K_{\mathrm{m}}=1400\right)\) and \((\mathrm{b})\) if the ring is made of silicon steel \(\left(K_{\mathrm{m}}=5200\right)\)

A toroidal solenoid with 400 turns of wire and a mean radius of 6.0 \(\mathrm{cm}\) carries a current of 0.25 A. The relative permeability of the core is \(80 .\) (a) What is the magnetic field in the core? (b) What part of the magnetic field is due to atomic currents?
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