c).Determine the dielectric constant of a membrane with electric field |E| = 10.

Question

c).Determine the dielectric constant of a membrane with electric field |E| = 10.47 x 106 V/m and area charge density ? = 8.41 x 10-4 C/m2.

Not that the result has no units. Express it to three significant figures. If you must use scientific notation, please enter as follows: e.g. 0.000123 = 1.23E-4. Only answer in numerical values, no units. For negative numbers, leave no space between the negative sign and the number: e.g. right: -1.00, wrong: - 1.00.


d.An air-filled capacitor with capacitance C = 3.32 µF carries a charge of Q = 22.7 µC on each plate. If the potential on the capacitor is produced by a battery, what is the potential of the battery?

Express the result in the unit [V] and to three significant figures. If you must use scientific notation, please enter as follows: e.g. 0.000123 = 1.23E-4. Only answer in numerical values, no units. For negative numbers, leave no space between the negative sign and the number: e.g. right: -1.00, wrong: - 1.00.

Explanation / Answer

The electric field E = 10.47*10^6 V/m The charge density = Q/A = 8.41*10^-4 C/m^2 The capacitor with dielectric          C = k 0A/d but C = Q/V so          Q/V = k 0A/d                 (Q/A) (d/V) = k 0            / E = k 0 therefore the dielectric constant            k = /E0               = (8.41*10^-4) / (10.47*10^6)(8.85*10^-12)               = 9.07 (d) The capacitance C = 3.32*10^-6F the charge Q = 22.7*10^-6 C then the potential          V = Q/C = (22.7*10^-6) / (3.32*10^-6)                          = 6.83 V    

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