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Answer :
Each sphere carries a charge of approximately 1130.973 nC or 1.130973 μC (microCoulombs).
The capacitance of a system consisting of two concentric conducting spheres can be determined using the formula:
C = (4πε₀) * (r₁ * r₂) / (r₂ - r₁),
where C is the capacitance, ε₀ is the vacuum permittivity constant (ε₀ = 8.99 × 10^9 N·m²/C²), r₁ is the radius of the inner sphere, and r₂ is the radius of the outer sphere.
Given the radii of the spheres as 5.0 cm and 10 cm, respectively, we can substitute these values into the formula to find the capacitance:
C = (4π * 8.99 × 10^9 N·m²/C²) * (0.05 m * 0.10 m) / (0.10 m - 0.05 m)
C = (4π * 8.99 × 10^9 N·m²/C²) * 0.005 m / 0.05 m
C = (4π * 8.99 × 10^9 N·m²/C²) * 0.1
C ≈ 4π * 8.99 × 10^8 N·m²/C²
Using the value of π (pi) as approximately 3.14159, we can evaluate the expression further:
C ≈ 4 * 3.14159 * 8.99 × 10^8 N·m²/C²
C ≈ 113.0973 × 10^8 N·m²/C²
C ≈ 1.130973 × 10^10 N·m²/C²
Therefore, the capacitance of this combination of spheres is approximately 1.130973 × 10^10 N·m²/C² or 11.30973 nF (nanoFarads).
To find the charge carried by each sphere, we can use the formula:
Q = C * V,
where Q is the charge, C is the capacitance, and V is the potential difference.
Substituting the values:
Q = (1.130973 × 10^10 N·m²/C²) * 100 V
Q ≈ 1.130973 × 10^12 N·m²/C
Q ≈ 1130.973 × 10^9 N·m²/C
Q ≈ 1130.973 nC (nanoCoulombs)
Hence, each sphere carries a charge of approximately 1130.973 nC or 1.130973 μC (microCoulombs).
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