Three Solid Plastic Cylinders Charge Calculation

Charge Calculation for Three Solid Plastic Cylinders

Three solid plastic cylinders all have radius 2.65 tm and length 6.06 cm. Find the charge of each cylinder given the following additional information about each one.

• Cylinder (s) carries charge with uniform density 15.7 nC/m² everywhere on its surface.
• Cylinder (b) carries charge with uniform density 157 nC/m³ on its curved lateral surface only.
• Cylinder (c) carries charge with uniform density 460 nC/m³ throughout the plastic c.

Final answer: The charge of each cylinder can be found using the formula q = σV. Cylinder (s) has a charge of approximately 24.9 nC, Cylinder (b) has a charge of approximately 788.7 nC, and Cylinder (c) has a charge of approximately 2302.1 nC.

Explanation

The charge of each cylinder can be found using the formula q = σV, where σ is the charge density and V is the volume of the cylinder. For Cylinder (s), the charge density is 15.7 nC/m² and the volume is given by V = πr²h, where r is the radius and h is the height. Substituting the values, we get qs = 15.7 × 10^-9 C/m² × π × (2.65 × 10^-2)² × (6.06 × 10^-2), which evaluates to approximately 24.9 nC. For Cylinder (b), the charge density is 157 nC/m³ and the volume is given by V = πr²h. The charge is then calculated as qb = 157 × 10^-9 C/m³ × π × (2.65 × 10^-2)² × (6.06 × 10^-2), which equals approximately 788.7 nC. For Cylinder (c), the charge density is 460 nC/m³ and the volume is given by V = πr²h. Plugging in the values, we find qc = 460 × 10^-9 C/m³ × π × (2.65 × 10^-2)² × (6.06 × 10^-2), which evaluates to approximately 2302.1 nC.