Three Solid Plastic Cylinders: A Fun Math Problem

What is the charge of each cylinder in the given data?

Given that the cylinders have the same radius and length, how can we calculate the charge of each cylinder based on the provided information?

Calculating the Charges of the Cylinders

Let's dive into the problem and calculate the charge of each cylinder in a fun and engaging way!

Charge Calculation:

Based on the data provided, we know that Cylinder (b) carries charge with uniform density of 15.0 nC/m² on its curved lateral surface only. We need to find the charge of the cylinder based on this information.

Using the formula for charge density: λ = Q / A, where λ is charge density, Q is charge, and A is surface area, we can calculate the charge of the cylinder.

Charge Density (λ) = 15 nC/m²

Radius (r) = 2.5 cm = 0.025 m

Length (L) = 6.0 cm = 0.06 m

First, let's find the curved surface area of the cylinder using the formula: A = 2πrL.

Calculating the surface area, we get: A = 9.43 x 10¯³ m².

Next, we can find the charge using the formula: Q = λ x A.

Substituting the values, we get: Q = 15 x 9.43 x 10¯³ = 0.141 nC.

Hence, the charge of the cylinder based on the given data is 0.141 nC.