Question

when a certain capacitor carries charge of magnitude q on each of its plates, it stores energy u. in order to store fourfold as much energy, how much charge should it have on its plates?

Answer 1

To store four times as much energy, the capacitor should have a charge of √(8U/C) on its plates.

Step-by-step explanation:

The energy stored in a capacitor is given by the expression Uc = Q²/(2C), where Uc is the energy stored, Q is the charge on the plates, and C is the capacitance of the capacitor. In order to store four times as much energy, we need to find the new value of charge, let's call it Q'.

Using the formula Uc = Q²/(2C), we have U' = Q'²/(2C), where U' represents the new energy. Since we want U' to be four times U, we can set up the equation U' = 4U:

4U = Q'²/(2C)

Q'² = 8U/C

Q' = √(8U/C). So, to store four times as much energy, the capacitor should have a charge of √(8U/C) on its plates.