Final answer:
To find the electric energy dissipated in the process of removing a square loop from a magnetic field, one must calculate the change in magnetic flux, use Faraday's Law to find the induced emf, calculate the induced current using Ohm's Law, and then use the formula for power dissipation to find the total energy dissipated.
Step-by-step explanation:
The question involves the concept of electromagnetic induction and energy dissipation in a resistor when the magnetic flux through a conducting loop changes. To calculate the electric energy dissipated during this process, several steps are followed:
- First, the magnetic flux (Φ) through the square loop must be computed using the formula Φ = B × A, where B is the magnetic field strength and A is the area of the loop.
- Next, we use Faraday's Law of Induction, which states that the induced electromotive force (emf) in a loop is equal to the negative rate of change of magnetic flux through the loop. The emf can be calculated using the formula emf = -ΔΦ/Δt where ΔΦ is the change in flux, and Δt is the change in time.
- Once the emf is known, the induced current (I) in the loop can be found using Ohm's Law, I = emf/R, where R is the resistance of the loop.
- Finally, the electric energy (E) dissipated in the resistor is given by E = I² × R × t, which is derived from the formula for power dissipated in a resistor P = I² × R, and energy is power multiplied by time.
By following these steps, we find that the electric energy dissipated in the square loop is given by: