A conducting loop of wire has an area of 150 cm² and a resistance of 25.0 Ω. There is a magnetic field of 100 T perpendicular to the loop. At what rate must this field be reduced to induce a current of 0.100 A in the loop? A) 167 T/s B) 60.0 T/s C) 5.58 T/s D) 0.354 T/s E) 120 T/s

Question

Quizplus · Accepted Answer

To induce a current of 0.100 A, the rate of change of magnetic flux (dΦ/dt) must equal the induced emf (ε), which is given by Ohm's Law as ε = IR = 0.100 A * 25.0 Ω = 2.5 V. The magnetic flux Φ = B * A, so dΦ/dt = A * dB/dt. Solving for dB/dt gives dB/dt = ε / A = 2.5 V / (150 cm² * 10⁻⁴ m²/cm²) = 167 T/s.

A Conducting Loop of Wire Has an Area of 150