Biology A red blood cell may carry an excess charge of about -2.5 ×10-12 C^-2.5 ×10^-12 C distri

step 1 For this problem on the topic of electrostatics, we are told that a red blood cell can carry an

Biology A red blood cell may carry an excess charge of about...

Biology A red blood cell may carry an excess charge of about $-2.5 \times 10-12 \mathrm{C}^{-2.5 \times 10^{-12} \mathrm{C}}$ distributed uniformly over its surface. The cells, modeled as spheres, are approximately $7.5 \mu \mathrm{m}$ in diameter and have a mass of $9.0 \times 10-14 \mathrm{~kg}^{9.0 \times 10^{-14} \mathrm{~kg} \text { . (a) How many excess electrons does a }}$ typical red blood cell carry? (b) What is the surface charge density $\sigma$ on the red blood cell? Express your answer in $\mathrm{C} / \mathrm{m}^{2}$ and in electrons $/ \mathrm{m}^{2}$. SSM Example 16-1

Key Concepts

Unit Conversion and Dimensional Analysis

Unit conversion and dimensional analysis ensure that all measurements are consistent and correctly applied in physical computations. When dealing with quantities expressed in different units (for example, micrometers for diameter or Coulombs for charge), it is important to convert them into coherent units (such as meters or standard SI units) to accurately compute derived quantities like the number of electrons or surface charge density.

Spherical Geometry

Spherical geometry is important in calculating the properties of objects modeled as spheres. In particular, the surface area of a sphere is given by 4?r², where r is the radius. This relation is essential when determining quantities like surface charge density, since the surface area directly impacts the distribution of charge over the object.

Charge Quantization

Charge quantization refers to the fact that electric charge comes in discrete amounts, typically as multiples of the elementary charge (the charge of a single electron). This concept is crucial because it allows one to determine the number of electrons corresponding to a given total charge by dividing the total charge by the elementary charge, ensuring that the net charge is an integer multiple of the electron's charge.

Surface Charge Density

Surface charge density is defined as the amount of electric charge per unit area on a surface. When a charge is uniformly distributed over a surface, such as on a sphere, the density is found by dividing the total charge by the total surface area of that sphere. This concept plays a vital role in understanding how charges are arranged on conductive or insulating surfaces and is key to solving problems related to charge distributions.

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