Final answer:
The induced electromotive force (emf) in a coil with 500 turns and square loops of side 10 cm, placed normal to a magnetic field increasing at 1 T/s, is calculated to be 5 V using Faraday's Law of Electromagnetic Induction.
Step-by-step explanation:
The question is asking about the induced electromotive force (emf) in a coil due to a changing magnetic flux. According to Faraday's Law of Electromagnetic Induction, the emf (ε) induced in a coil is equal to the negative change in magnetic flux (ΔΦ) through the coil over time (Δt), multiplied by the number of turns (N) in the coil, which is expressed as ε = -N (ΔΦ/Δt). In this case, the coil has 500 turns and is placed normal to the magnetic field.
The side of each square loop is given as 10 cm, so the area (A) of one loop is A = (0.10 m) x (0.10 m) = 0.01 m². The magnetic flux is increasing at a rate of 1 T/s (tesla per second), so ΔB/Δt = 1 T/s. The total change in flux through one loop over time is ΔΦ = A * ΔB/Δt = 0.01 m² * 1 T/s, which gives us a flux change of 0.01 weber per second. Therefore, the induced emf for 500 loops is ε = -500 * 0.01 V/s = -5 V. The negative sign indicates the direction of the emf which, according to Lenz's law, opposes the change in flux.