The Magnitude of Charge on a Capacitor

Understanding Capacitor Charge Calculation

A capacitor is made from two hollow, coaxial, iron cylinders; one inside the other. The inner cylinder is negatively charged, and the outer is positively charged. The potential difference between the two cylinders is 2.30 V. The inner cylinder has a radius of 5.00 mm, the outer one has a radius of 18.0 mm, and the length of each cylinder is 0.500 m.

Calculation of Charge on Each Cylinder

What is the magnitude of the charge on each of the cylinders?

a) 1.79 pC
b) 10.0 pC
c) 27.8 pC
d) 49.9 pC
e) 100 pC
f) answer not given

Final answer: The magnitude of the charge on each of the cylinders is not given (f).

Explanation: To calculate the charge on each cylinder, we can use the formula Q = CV, where Q is the charge, C is the capacitance, and V is the potential difference. First, let's calculate the capacitance of the capacitor. Since the cylinders can be approximated as parallel plates, we can use the formula C = ε₀A/d, where ε₀ is the permittivity of free space, A is the area of the plates, and d is the distance between the plates.

The area of the plates can be calculated as the difference between the areas of the outer and inner cylinders: A = π(r₂² - r₁²), where r₂ is the radius of the outer cylinder, and r₁ is the radius of the inner cylinder. Substituting the given values, we have:

A = π((18.0 mm)² - (5.00 mm)²)

Next, we need to convert the radii to meters: A = π((0.018 m)² - (0.005 m)²)

Now, let's calculate the distance between the plates. Since the cylinders are coaxial, the distance between the plates is the difference in their lengths: d = l₂ - l₁, where l₂ is the length of the outer cylinder, and l₁ is the length of the inner cylinder. Substituting the given values, we have:

d = 0.500 m - 0.500 m = 0 m

Since the distance between the plates is 0, the capacitance becomes infinite. This means that the charge on each cylinder is also infinite. Therefore, the answer is not given (f).