Final answer:
The self-inductance of the solenoid needs to be 8.0 henries to store 16.0 joules of energy when a current of 2.00 amperes is flowing through it.
Step-by-step explanation:
The question asks about the self-inductance of a solenoid required to store a certain amount of energy when a specific current runs through it. The energy (E) stored in an inductor (or solenoid) can be expressed using the formula E = (1/2) * L * I2, where E is the stored energy, L is the inductance, and I is the current. Given that the energy to be stored is 16.0 J and the current is 2.00 A, we can rearrange the formula to solve for L: L = 2E/I2.
Plugging in the given values: L = 2 * 16.0 J / (2.00 A)2 = 32.0 J / 4.00 A2 = 8.0 H (henries). Therefore, the self-inductance of the solenoid needs to be 8.0 henries to store 16.0 joules of energy with a current of 2.00 amperes flowing through it.