Final answer:
The induced emf in a square-shaped coil with 100 turns, each side being 10 cm, placed in a magnetic field that is increasing at a rate of 1 T/s, is calculated using Faraday's Law and is found to be 1 V. Therefore, the correct answer is (a) 1 V.
Step-by-step explanation:
The question relates to electromagnetism, specifically Faraday's Law of electromagnetic induction. Faraday's Law states that the induced electromotive force (emf) in any closed circuit is equal to the negative of the time rate of change of the magnetic flux through the circuit.
The induced emf (E) can be calculated using the formula
E = -N * (dΦ / dt),
where N is the number of turns in the coil, and (dΦ / dt) is the rate of change of magnetic flux through the coil.
To find the induced emf in the square-shaped coil, we use the coil's dimensions (given as 10 cm per side) and the rate of change of the magnetic field (given as 1 T/s). Since the sides of the square are 0.1 meters (converted from 10 cm), the area (A) of the coil is A = (side)² = (0.1 m)² = 0.01 m².
The rate of change of magnetic flux is then given by
(dΦ / dt) = A * (dB/dt) = 0.01 m² * 1 T/s = 0.01 T * m²/s.
For 100 turns, the induced emf is
E = -N * (dΦ / dt) = -100 turns * 0.01 T * m²/s = -1 V.
The negative sign indicates the emf's direction (opposing the change in flux), but since only the absolute value is required, the induced emf is 1 V.
Therefore, the induced emf in the coil is 1 V, making the answer (a) 1 V.