A capacitor consists of two concentric spherical shells. The outer radius of the inner shell is a=0.76 mm and the inner radius of the outer shell is b=3.31 mm .
(a) What is the capacitance C of this capacitor? Express your answer in Farads.
unanswered
(b) Suppose the Maximum possible electric field at the outer surface of the inner shell before the air starts to ionize is Emax(a)=3.0×106V⋅m-1 . What is the maximum possible charge on the inner sphere? Express your answer in Coulombs.
unanswered
(c) What is the maximum amount of energy stored in the capacitor? Express your answer in Joules.
unanswered
(d) When E(a)=3.0×106V⋅m-1 what is the absolute value of the potential difference between the shells? Express your answer in Volts.
To find the absolute value of the potential difference between the shells, we can use the formula:
V = E * d
Where V is the potential difference, E is the electric field, and d is the distance between the shells.
In this case, the electric field at the outer surface of the inner shell is given as E(a) = 3.0×10^6 V*m^(-1). The distance between the shells can be calculated as the difference between the inner radius of the outer shell and the outer radius of the inner shell:
d = b - a = 3.31 mm - 0.76 mm = 2.55 mm = 2.55 × 10^(-3) m
Now we can substitute the values into the formula:
V = (3.0×10^6 V*m^(-1)) * (2.55 × 10^(-3) m)
V = 7.65 V
Therefore, when the electric field is 3.0×10^6 V*m^(-1), the absolute value of the potential difference between the shells is 7.65 Volts.
To find the potential difference between the shells, we can use the formula relating electric field to potential difference:
E = V / r
Where E is the electric field, V is the potential difference, and r is the radius.
Given that E(a) = 3.0 × 10^6 V·m^(-1) and a = 0.76 mm, we can rearrange the formula to solve for V:
V = E(a) * a
V = 3.0 × 10^6 V·m^(-1) * 0.76 × 10^(-3) m
V = 2.28 V
Therefore, the absolute value of the potential difference between the shells is 2.28 Volts.