Final answer:
To induce a current of 0.07 A in the rectangular coil, the rate of change of the magnetic field is determined using Faraday's Law of Induction and Ohm's Law, considering the coil's area, number of turns, and total resistance.
Step-by-step explanation:
To find the rate at which the magnitude of the magnetic field B must change to induce a current of 0.07 A in a rectangular coil with 70 turns and a resistance of 5.2 ω, we use Faraday's Law of Induction and Ohm's Law. The induced emf (ε) in the coil is given by Faraday's Law:
ε = N × (dΦ/dt)
where Φ is the magnetic flux, N is the number of turns, and dΦ/dt is the rate of change of magnetic flux. Since the coil is perpendicular to the magnetic field, Φ = B × A, where A is the area of the coil. For a rectangular coil with sides of lengths 3.5 cm and 4.6 cm, the area A = 3.5 cm × 4.6 cm = 0.035 m × 0.046 m.
The induced emf is also related to the induced current (I) and resistance (R) by Ohm's Law:
ε = I × R
Combining these equations and solving for dΦ/dt gives:
dΦ/dt = (I × R) / (N × A)
Plugging in the given values:
dΦ/dt = (0.07 A × 5.2 ω) / (70 × 0.035 m × 0.046 m)
After calculating, we get the rate at which the magnetic field must change which answers the question.