Positive electric charge Q = 5.0 mu C is distributed uniformly through the volum
ID: 1418376 • Letter: P
Question
Positive electric charge Q = 5.0 mu C is distributed uniformly through the volume of a spherical insulator with radius of = 1.0 cm. Find the electric field inside and outside of the sphere. Assume the permittivity of insulator is the same as the permittivity of the free space. The resting potential difference across a cell membrane from outside to inside is initially at -90 mV. When a simulated is applied, Na^+ ions are moved into the cell such that the potential changes to +20 mV for a short time. Assume the dielectric constant through the membrane is 4. If the membrane capacitance per unit area is 1 mu F/cm^2, how much charge moves through a membrane of area 0.05 cm^2? Find the membrane thickness. The charge on Na^+ is +e. How many ions move through the membrane? Find the total work that is needed to transport this amount sodium ions cross the membrane.Explanation / Answer
1.
Electric field r > a (i.e. outside)
E = [1/4*pi*0)* Q/r^2
= 9*10^9*5*10^-6/r^2
= 4.5*10^4/r^2.
For r<1 cm
E = K*Q'/r^2
Q' is the charge contained by spher of r radius,
Q'/Q = r^3/1^3*10^-6
Q' = 10^6*r^3*Q, where r is in meteres.
E = 9*10^9*10^6*r^3*Q/r^2
= 9*10^9*10^6*r^3*5*10^-6/r^2
=(4.5*10^10)*r