You discover a bacterium. In the microscope it looks like aball 4.00 x 10 -2 mm

Question

You discover a bacterium. In the microscope it looks like aball 4.00 x 10-2 mm in diameter surrounded with amembrane 6 nm thick. The membrane material has a dielectricconstant of 8.00 and a dielectric strength of 2.00 x107V/m. a. What is the capacitance of the bacterium? b. If the electric potential increased by 50 mV from inside tooutside the bacterium, what is the charge on the outer surface ofthe bacterium? c. What is the number of positive ions (H+)associated with the bacterium? d. What is the maximum potential difference that can beapplied across the membrane? You discover a bacterium. In the microscope it looks like aball 4.00 x 10-2 mm in diameter surrounded with amembrane 6 nm thick. The membrane material has a dielectricconstant of 8.00 and a dielectric strength of 2.00 x107V/m. a. What is the capacitance of the bacterium? b. If the electric potential increased by 50 mV from inside tooutside the bacterium, what is the charge on the outer surface ofthe bacterium? c. What is the number of positive ions (H+)associated with the bacterium? d. What is the maximum potential difference that can beapplied across the membrane?

Explanation / Answer

Just incase...
D= 4.00 x 10-2 mm = 4.00 x 10-5 m
d=6 nm = 6x10-9m
r= 8.00
0 = 8.854x10-12 F/m
k= 2.00 x 107V/m.

a. What is the capacitance of the bacterium?
C= r r A/d
A= 4(D/2)2
C= r r4(D/2)2/d
C=4 8.00 x 8.854x10-12 (4.00 x 10-5/2)2/6x10-9 =

b. If the electric potential increased by 50 mV from inside tooutside the bacterium, what is the charge on the outer surface ofthe bacterium?
Q=CV
.
c. What is the number of positive ions (H+)associated with the bacterium?
N= Q/q
q=1.602 x10-19C
.
d. What is the maximum potential difference that can beapplied across the membrane?
Vmax= kd

Just plug and play
Let me know if you have any problems.

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