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Chapter 20: Problem 4

Electric Potential Across a Cell Membrane In a typical living cell, the electric potential inside the cell is \(0.070 \mathrm{V}\) lower than the electric potential outside the cell. The thickness of the cell membrane is \(0.10 \mu \mathrm{m}\). What are the magnitude and direction of the electric field within the cell membrane?

Short Answer

Expert verified
The electric field magnitude is 700,000 V/m, directed inward.

Step by step solution

01

Understanding the Problem

We are given that the electric potential inside a cell is 0.070 V lower compared to the outside. Also, the thickness of the cell membrane is 0.10 碌m, which we will convert to meters (0.10 碌m = 0.10 x 10^{-6} m). We need to calculate the magnitude and direction of the electric field inside the cell membrane.
02

Using the Formula for Electric Field

The electric field (E) can be calculated using the formula \( E = \frac{V}{d} \), where V is the potential difference, and d is the separation (thickness of the membrane in this case).
03

Substitute Known Values

Substitute 0.070 V for the potential difference (V) and 0.10 x 10^{-6} m for d in the equation: \(E = \frac{0.070}{0.10 \times 10^{-6}}\).
04

Solve for Electric Field Magnitude

Calculate the magnitude of the electric field: \(E = \frac{0.070}{0.10 \times 10^{-6}} = 700,000 \mathrm{V/m}\). This value represents the strength of the electric field.
05

Determine the Direction of Electric Field

Since the potential is higher outside the cell, the electric field points from the outside to the inside. Therefore, the electric field direction is inward.

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Key Concepts

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

Electric Potential
Electric potential, often referred to as voltage, is a measure of the potential energy per unit charge at a specific point in an electric field. It tells us how much energy would be given to a positive charge if it were moved from one point to another within the field. In the context of a cell, this electric potential is critical because it influences how ions move across the cell membrane, impacting cellular function.
  • In cells, the electric potential is often determined by the distribution of ions, such as sodium and potassium, across the membrane.
  • The difference in electric potential between the inside and outside of a cell is essential for activities like nerve conduction and muscle contraction.
By understanding the electric potential in a cell, we can better comprehend how electrical signals are propagated, which is fundamental in both biology and medical fields.
Cell Membrane
The cell membrane is a crucial component of living organisms, acting as a barrier to protect the internal environment of the cell. It鈥檚 selectively permeable, allowing certain substances to enter or leave the cell, thereby maintaining homeostasis.
  • A typical cell membrane is only about 0.10 micrometers thick, which is around 10,000 times thinner than a sheet of paper.
  • This thin barrier plays a significant role in managing the electric potential by controlling the passage of ions.
Besides its protective role, the cell membrane is involved in communication between cells and in signaling pathways that drive cell responses to various stimuli.
Potential Difference
Potential difference, often termed voltage difference, is the measure of the energy difference per charge between two points in an electric field. In cells, this potential difference exists across the cell membrane and is crucial for cellular processes.
  • The potential difference is due to varying concentrations of ions across the membrane, often maintained by ion pumps and channels.
  • Typically, the inside of the cell has a lower electric potential by about 0.070 V compared to the outside, as mentioned in the exercise.
This potential difference facilitates the transport of ions and other molecules, thus contributing to essential physiological processes like muscle movement and nerve impulse transmission.
Electric Field Direction
The direction of the electric field is always from regions of higher potential to lower potential. Inside a biological cell, this means the electric field's direction is typically from the outside of the cell membrane to the inside, due to the higher potential outside.
  • The direction of the electric field is critical, as it influences how ions move across the membrane.
  • The electric field inside the membrane not only affects the movement of ions but also is key to maintaining the membrane's resting potential.
Understanding the direction of the electric field helps us to predict the behavior of charge carriers within biological systems, which can be applied in fields such as neuroscience and pharmacology.

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Most popular questions from this chapter

The electrons in a TV picture tube are accelerated from rest through a potential difference of \(25 \mathrm{kV}\). What is the speed of the electrons after they have been accelerated by this potential difference?

Consider a region in space where a uniform electric field \(E=6500 \mathrm{N} / \mathrm{C}\) points in the negative \(x\) direction. (a) What is the orientation of the equipotential surfaces? Explain. (b) If you move in the positive \(x\) direction, does the electric potential increase or decrease? Explain. (c) What is the distance between the \(+14-V\) and the \(+16-V\) equipotentials?

A parallel-plate capacitor is constructed with circular plates of radius \(0.056 \mathrm{m}\). The plates are separated by \(0.25 \mathrm{mm}\), and the space between the plates is filled with a dielectric with dielectric constant \(\kappa .\) When the charge on the capacitor is \(1.2 \mu C\) the potential difference between the plates is 750 V. Find the value of the dielectric constant, \(\kappa\).

Predict/Explain A positive charge is moved from one location on an equipotential to another point on the same equipotential. (a) Is the work done on the charge positive, negative, or zero? (b) Choose the best explanation from among the following: I. The electric field is perpendicular to an equipotential, therefore the work done in moving along an equipotential is zero. II. Because the charge is positive the work done on it is also positive. III. It takes negative work to keep the positive charge from accelerating as it moves along the equipotential.

A uniform electric field of magnitude \(6.8 \times 10^{5} \mathrm{N} / \mathrm{C}\) points in the positive \(x\) direction. Find the change in electric potential between the origin and the points (a) \((0,6.0 \mathrm{m})\) (b) \((6.0 \mathrm{m}, 0)\) and (c) \((6.0 \mathrm{m}, 6.0 \mathrm{m})\)
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