A spherical capacitor has an inner radius of 8.00 mmand an outer radius of 8.50

Question

A spherical capacitor has an inner radius of 8.00 mmand an outer radius of 8.50 mm. With air between the spheres, the capacitor is connected to a battery and allowed to charge fully. With the battery still connected, oil is poured in, filling the volume between the spheres. As the oil is added, the battery does an additional8.30 nJ of work on the capacitor. Suppose that the dielectric constant of the oil is oil = 4.5.

What is the potential difference supplied by the battery?

Express your answer with the appropriate units.

Explanation / Answer

inner radius R1=8.00mm

outer radius R2=8.50mm

E=8.30nj=8.3*10-9

I=4.5

therefore the potential difference v1=E-IR1

=(8.3*10-9)-(4.5*(8*10-3))

=-0.035

v2=(8.3*10-9)-(4.5*(8.5*10-3))

=-0.03824

therefore v=v1-v2

=(-0.035)-(-0.03824)

=3.24*10-3m

=3.24mm

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