Finding the Charge of Three Solid Plastic Cylinders

Calculating the Charge of Each Cylinder

Three solid plastic cylinders all have a radius of 2.45 cm and a length of 6.36 cm. We need to find the charge of each cylinder based on the following additional information:

Cylinder (a) carries charge with uniform density 15.3 nC/m² everywhere on its surface.

Cylinder (b) carries charge with uniform density 15.3 nC/m² on its curved lateral surface only.

Cylinder (c) carries charge with uniform density 490 nC/m³ throughout the plastic.

The charge on cylinder (a) with the given uniform density is calculated to be 0.16366 m².

The charge on cylinder (b) with uniform density on the curved lateral surface only is calculated to be 0.1499 m².

The charge on cylinder (c) with the given uniform density is calculated to be 0.049 nc.

Given data:

Radius of the cylinder = 2.45 cm = 0.0245 m

Length = 6.36 cm = 0.0636 m

Charge density λ = 15.3 nC/m²

The surface area of the cylinder is calculated as:

Surface area = 2π r L + 2π r² = 2π × 0.0245 × 0.0636 + 2π × 0.0245 m² = 0.0098 + 0.15386 m² = 0.16366 m²

To find the charge, we use the relation:

Q = λ A = 15.3 × 0.16366 = 2.51 nc

The charge on cylinder (b) with uniform density on the curved lateral surface is calculated as:

Surface area = 2π r L = 0.0098 m²

Q = λ A = 15.3 × 0.0098 = 0.1499 nc

The charge on cylinder (c) with uniform density is calculated as:

Q = 490 × 0.0636 = 31.164 × 2π r = 0.049 nc

What is the charge on each of the three solid plastic cylinders with the given parameters?

The charge on cylinder (a) is 2.51 nc, the charge on cylinder (b) is 0.1499 nc, and the charge on cylinder (c) is 0.049 nc.