What is the charge of each cylinder given the information provided?

Question

Carmen · Answer

Calculating Charge of Each Cylinder: Each of the three solid plastic cylinders has a radius of 2.73 cm and a length of 6.48 cm. Cylinder (a) has a charge with uniform density of 13.7 nC/m² on its entire surface, cylinder (b) has a charge with uniform density of 13.7 nC/m² only on its curved lateral surface, and cylinder (c) has a charge with uniform density of 490 nC/m³ throughout the plastic.  The surface area of each cylinder can be calculated using the formula: S = 2πrh + 2πr², where h is the height and r is the radius of the cylinder. Substituting the values, we get: S = 2π(2.73)(6.48) + 2π(2.73)² S = 106.822 + 59.049 S = 165.871 cm².  The volume of each cylinder can be calculated as V = πr²h. For cylinder (c), the charge Q can be calculated using the formula Q = ρV, where ρ is the charge density and V is the volume of the cylinder: Q = (490 nC/m³) × π(2.73 cm)²(6.48 cm) Q = 584.634 nC.  For cylinder (a), the charge Q is uniformly distributed across the surface and can be calculated using the formula Q = σS, where σ is the surface charge density and S is the surface area of the cylinder: Q = (13.7 nC/m²) × (165.871 cm² / (100 cm/m)²) Q = 22.747 nC.  For cylinder (b), the charge Q is only on its curved lateral surface. The surface area to be used in the formula for cylinder (b) is the curved lateral surface area: Q = (13.7 nC/m²) × (106.822 cm² / (100 cm/m)²) Q = 14.655 nC.  Therefore, the charge of each cylinder is 584.634 nC for cylinder (c), 22.747 nC for cylinder (a), and 14.655 nC for cylinder (b).

Three Solid Plastic Cylinders: Charge Calculations

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