When a 360 nF air capacitor is connected to a power supply, the energy stored in the capacitor is 1.85 x 10-5 J. While the capac
itor is kept connected to the power supply, a slab of dielectric is inserted that completely fills the space between the plates. This increases the stored energy by 2.32 x 10-5 J. (a) What is the potential difference between the capacitor plates
Let denote the capacitance of a capacitor. Let be the potential difference (voltage) between the two plates of this capacitor. The energy stored in this capacitor would be:
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Rearrange this equation to find an expression for the potential difference in terms of capacitance and energy :
.
The capacitance of this capacitor is given in nanofarads. Convert that unit to standard unit (farads):
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Given that the energy stored in this capacitor is , the potential difference across the capacitor plates would be:
It is required to find the orbital period of a dwarf planet. Let T is time period. The relation between the time period and the semi major axis is given by Kepler's third law. Its mathematical form is given by :
G is universal gravitational constant
M is solar mass
Plugging all the values,
Since,
So, the orbital period of a dwarf planet is 138.52 years.