Intermediate Physics for Medicine and Biology  Russell K. Hobbie & Bradley J. Roth
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Problems 
249 

Symbol 
Use 
Units 
First 
0 


Electrical permittivity 
C2 
N−1 
229 




used on 



of vacuum 


m−2 





page 
κ 


Dielectric constant 



229 

p, pc, po 
Probability 

240 
η 


Coe cient of viscocity 
Pa s 
248 

q 
Charge 
C 
233 
λD 


Debye length 

m 

230 

r, r 
Position 
m 
229 
λ 


Characteristic length 

m 

235 

r 
Radius in cylindrical co 
m 
236 
ν 


Frequency 


Hz or s−1 
244 


ordinates 


ρ, ρext 

Charge density 

C m−3 
229 

r 
Radius in spherical coor 
m 
232 
ρ 


Resistivity 


Ω m 
235 


dinates 


σq , σq 

Charge per unit area 

C m−2 
233 

t 
Time 
s 
242 
σ 


Conductivity 

S m−1 
235 

u 
rv(r) 
V m 
232 
σi 


Standard 
deviation 
of 
A 

242 

u, uo 
Energy (normalized to 

235 



current 






v, v 
kB T ) 


σn 


Standard 
deviation 
of 


242 

Potential 
V 
227 



number of ions 





vNernst 
Nernst potential 
V 
236 
σq 


Standard deviation of 
C 

242 

w 
Energy 
J 
240 



charge 






x 
Position 
m 
229 
σq 


Charge per unit area 

C m−2 
246 

x 
Distance along 
m 
236 
σv 


Standard deviation of 
V 

242 


cylindrical axis 





voltage 






z 
Valence 

227 
τ 


Time constant 

s 

235 

A, B, A , B 
Constants 
V 
231 
τ 


Torque 


N m 
248 

Bearth 
Earth’s magnetic ﬁeld 
T 
247 
τt 


Tissue time constant 

s 

246 

B0 
Amplitude of applied os 
T 
248 
θ 


Angle 




248 


cillating magnetic ﬁeld 


φ 


Angle in cylindrical 



236 

C, C 
Concentration 
m−3 
227 



coordinates 





Ci 
Concentration of species 
m−3 
230 
χ 


Susceptibility 

N−1 s−1 
234 

[Cl] , [Cl ] 
i 
m−3 

ω, ωs, ω0 
Solute permeability 

237 

Chloride concentration 
228 
ω 


Angular frequency 

s−1 
246 

C 
Capacitance 
F 
242 
ωt 


Characteristic angular 
s−1 


D, De , D0 
Di usion constant 
m2 s−1 
234 



frequency of tissue 





E, Ex, E0, E1 
Electric ﬁeld 
V m−1 
229 
ξ 


Energy in units of kB T 


230 

Eext 
External electric ﬁeld 
V m−1 
234 
Γ 


Radial concentration 



236 

Epol 
Polarization electric 
V m−1 
233 



factor 







ﬁeld 












E 
Photon energy 
J 
244 
Problems 






F 
Faraday constant 
C mol−1 
227 






F, F 
Force 
N 
234 










G 
Conductance 
S 
235 
Section 9.1 






J 
Current per unit area of 
A m−2 
237 
















[K] , [K ] 
membrane 
m−3 

Problem 1 The chloride ratio between plasma and in 

Potassium 
228 
terstitial ﬂuid is 0.95. Plasma protein has a valence of 


concentration 



L 
m 
235 
about 
− 
18. In the interstitial ﬂuid, Na = Cl = 155 

Separation 









M+ , M+ 
Concentration of imper 
m−3 
228 
mmol l−1. Find the sodium, chloride and protein concen 

M− , M− 
meant cations 
m−3 

trations in the plasma and the potential di erence across 

Concentration of imper 
228 
the capillary wall, assuming Donnan equilibrium. 



meant anions 












[M] , [M ] 
Net concentration of im 
m−3 
228 
Problem 2 Suppose that there are 
two 
compartments 


permeant ions 






with equal volume V = 1 l, separated by a membrane that 

N 
Number per unit volume 
m−3 
233 

NA 
Avogadro’s number 
mol−1 
234 
is permeable to K and Cl ions. Impermeant positive ions 

[Na] , [Na ] 
Sodium concentration 
m−3 
228 
have a concentration 0 on the left and M = M+ =10 

P 
Polarization 
C m−2 
234 
mmol l−1 on the right. The initial concentration of potas 

R 
Gas constant 
J K−1 
227 
sium is [K0] = 30 mmol l−1 on the left. T = 310 K. 




mol−1 






(a) Find 
the initial concentrations 
of potassium 
and 

R 
Resistance 
Ω 
235 

chloride on both sides and the potential di erence. 


Rp 
Pore radius 
m 
236 


S 
Area 
m2 
229 
(b) A ﬁxed amount of potassium chloride (10 mmol) is 

T 
Temperature 
K 
227 
added on the left. After things have come to equilibrium, 

U, W 
Energy 
J 
242 
ﬁnd the new concentrations and potential di erence. 


V 
Particle velocity 
m s−1 
234 












α 
Proportionality 

240 
Problem 3 The extracellular space in cartilage contains 


constant 






large, immobile, negatively charged molecules called gly 

β 
Linear viscous drag coef 
N s m−1 
234 


ﬁcient 


coaminoglycans (GAGs). An early sign of osteoarthritis 

β 
Rotational viscous drag 
N s m 
248 
is the loss of GAGs. The concentration of the GAGs is 


coe cient 


di cult to 
measure directly, but 
Shapiro 
et al. (2002) 
























References 
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Problem 33 Electric ﬁelds in the body caused by expo 
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Problem 34 Derive the equations for the electric ﬁeld 
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in Fig. 
9.19. Use 
the following 
method. 
Let 

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σ 







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∂r 










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∂r 

















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b 




















r=a 

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