Answer :
The rate of change of the magnetic field, dB/dt, required to induce a 10 A current in the circular loop can be calculated using Faraday's law of electromagnetic induction:
dB/dt = (2πR²I)/(πr²)
where R is the radius of the loop (5 cm), r is the radius of the wire (1.25 mm), and I is the current induced (10 A).
Substituting the values, we get:
dB/dt = (2π(0.05)²(10))/(π(0.00125)²) = 254904.67 T/s
Therefore, the magnitude of the magnetic field must be changing at a rate of approximately 254.9 kT/s to induce a 10 A current in the circular loop.
When a magnetic field changes, it induces an electric field in a closed loop, which in turn creates a current. This is known as Faraday's law of electromagnetic induction. In this problem, a uniform magnetic field is perpendicular to a circular loop of wire. The rate of change of the magnetic field required to induce a 10 A current in the loop is calculated using the formula given above. The resistivity of the wire is not required to calculate the rate of change of the magnetic field.
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