Final answer:
To store 4.0 joules of energy, a 1.0 μF capacitor should be charged to approximately 2828.43 volts, based on the formula E = 1/2 CV^2, where E is energy, C is capacitance and V is potential.
Step-by-step explanation:
To determine the potential to which a capacitor should be charged to store a specific amount of energy, we can use the formula for the energy stored in a capacitor:
E = 1/2 C V2
Where E is the energy in joules, C is the capacitance in farads, and V is the potential in volts.
First, let's rearrange the formula to solve for V:
V = √(2 E / C)
Given that the energy E is 4.0 J and the capacitance C is 1.0 μF (which is 1.0 x 10-6 F), we can substitute these values into the equation:
V = √(2 * 4.0 J / 1.0 x 10-6 F)
Calculating this gives us:
V = √(8 x 106 J/F)
V = 2828.43 V
Therefore, the capacitor should be charged to approximately 2828.43 volts to store 4.0 joules of energy.