Final answer:
To find the charge on each electrode of a parallel-plate capacitor, you need to use the formula Q = CV, where Q is the charge, C is the capacitance, and V is the electric potential difference. Calculate the capacitance using the formula C = ε₀A/d, then multiply the capacitance by the electric field strength to find the charge on each electrode. The charge on each electrode of this capacitor is 75.0 nC.
Step-by-step explanation:
To find the charge on each electrode of a parallel-plate capacitor, you need to use the formula Q = CV, where Q is the charge, C is the capacitance, and V is the electric potential difference. First, calculate the capacitance using the formula C = ε₀A/d, where ε₀ is the vacuum permittivity, A is the area of the electrodes, and d is the distance between them. Then, multiply the capacitance by the electric field strength to find the charge on each electrode.
In this case, the diameter of the electrodes is 9.1 cm, so the area can be found as A = π(r^2) = π(4.55^2) cm². Convert the area to m² by dividing by 10000. The distance between the electrodes is 1.3 mm, which is equal to 0.0013 m. Substitute the values into the capacitance formula:
C = (8.85x10^-12 F/m)(π(4.55x10^-2 m)^2)/(0.0013 m) = 1.50x10^-11 F
Then, multiply the capacitance by the electric field strength of 5.0x10^6 N/C:
Q = (1.50x10^-11 F)(5.0x10^6 N/C) = 7.50x10^-5 C
Finally, convert the charge to nanocoulombs by multiplying by 10^9:
Q = 7.50x10^-5 C x 10^9 nC/C = 75.0 nC