Final answer:
The average power dissipation in a loop due to an oscillating current cannot be calculated without additional information regarding the magnetic field and its change over time. Necessary formulas such as Faraday's Law and Ohm's Law are mentioned, but cannot be applied without missing details.
Step-by-step explanation:
The question asks us to calculate the average power Pavg dissipated by a copper loop due to its proximity to a sinusoidally oscillating current in a wire. To find the average power, we must first determine the magnetic field caused by the wire, the induced electromotive force (EMF) in the loop, and the induced current, before we can apply the formula for power dissipation in a resistor.
However, the question does not provide enough information to directly calculate the average power without making certain assumptions. We would typically use Faraday's law to calculate the induced EMF, which depends on the time rate of change of the magnetic field experienced by the loop. Unfortunately, without the specific magnetic field as a function of time or distance, or the rate at which the magnetic field is changing, we cannot calculate the EMF. Once the EMF is known, Ohm's Law (V = IR) could be used to find the induced current (I), if the resistance (R) of the loop is known. Power can then be calculated using the formula P = I2R, where I is the rms (root mean square) of the induced current.
As the question stands, important information for calculation seems to be omitted, and so a numerical answer cannot be provided without further details or assumptions.