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A conducting sphere of diameter 20 cm is charged to a potential of 80,000V with respect to earth potential. Calculate the charge on the sphere assuming it to be situated in air.

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8.90×10−7 C\text{8.90} \times 10^{-7} \text{ C}

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Here's the solution for .7:

1.7) A conducting sphere of diameter 20 cm is charged to a potential of 80,000V with respect to earth potential. Calculate the charge on the sphere assuming it to be situated in air.

Given values:
Diameter, D=20 cm=0.20 mD = 20 \text{ cm} = 0.20 \text{ m}
Radius, r=D2=0.20 m2=0.10 mr = \frac{D}{2} = \frac{0.20 \text{ m}}{2} = 0.10 \text{ m}
Potential, V=80,000 VV = 80,000 \text{ V}
Permittivity of free space, ϵ0=8.85×10−12 F/m\epsilon_0 = 8.85 \times 10^{-12} \text{ F/m}

  1. Calculate the capacitance of an isolated conducting sphere.

    The capacitance CC of an isolated conducting sphere in air (or vacuum) is given by the formula:

    C=4πϵ0rC = 4 \pi \epsilon_0 r

  2. Substitute the values into the capacitance formula.

    C=4π(8.85×10−12 F/m)(0.10 m)C = 4 \pi (8.85 \times 10^{-12} \text{ F/m}) (0.10 \text{ m}) C≈1.112×10−11 FC \approx 1.112 \times 10^{-11} \text{ F}

  3. Calculate the charge on the sphere using the relationship Q=CVQ = CV.

    Q=(1.112×10−11 F)×(80,000 V)Q = (1.112 \times 10^{-11} \text{ F}) \times (80,000 \text{ V}) Q=8.896×10−7 CQ = 8.896 \times 10^{-7} \text{ C}

    The charge on the sphere is 8.90×10−7 C\text{8.90} \times 10^{-7} \text{ C}.

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