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A metal sphere with radius ra = 1.30cm is supported on an insulating stand at the center of a hollow, metal, spherical shell with radius rb = 9.90cm . Charge +q is put on the inner sphere and charge ?q on the outer spherical shell. The magnitude of q is chosen to make the potential difference between the spheres 480V , with the inner sphere at higher potential.

Part A

Calculate q.
q =................C

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Answer:

[tex]7.9902734304\times 10^{-10}\ C[/tex]

Explanation:

k = Coulomb constant = [tex]8.99\times 10^{9}\ Nm^2/C^2[/tex]

[tex]r_1[/tex] = 1.3 cm

[tex]r_2[/tex] = 9.9 cm

V = Voltage = 480 V

Potential difference is given by

[tex]V=kq(\dfrac{1}{r_1}-\dfrac{1}{r_2})\\\Rightarrow q=\dfrac{V}{k(\dfrac{1}{r_1}-\dfrac{1}{r_2})}\\\Rightarrow q=\dfrac{480}{8.99\times 10^{9}\times(\dfrac{1}{0.013}-\dfrac{1}{0.099})}\\\Rightarrow q=7.9902734304\times 10^{-10}\ C[/tex]

The charge is [tex]7.9902734304\times 10^{-10}\ C[/tex]

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