Final answer:
To determine the induced EMF in a loop with a diameter of (1.10×10⁻¹)m in a magnetic field that is increasing at (2.0×10⁻¹)T/s, we use Faraday's Law and calculate the area of the loop to find the change in magnetic flux and thus the induced EMF.
Step-by-step explanation:
To calculate the induced electromotive force (EMF) in a loop with a diameter of (1.10×10⁻¹)m due to a changing magnetic field that is increasing at a rate of (2.0×10⁻¹)T/s, we can use Faraday's Law of electromagnetic induction. Faraday's Law states that the induced EMF (ε) in a loop is equal to the negative rate of change of magnetic flux through the loop.
First, we calculate the area (A) of the loop, which is a circle. The formula for the area of a circle is A = πr^2, where r is the radius. The radius is half of the diameter, so for our loop, r = (1.10×10⁻¹ m) / 2. Using π ≈ 3.14, we have A = π * (0.55×10⁻¹ m)^2.
Next, according to Faraday's Law, the induced EMF is calculated using ε = -N * dΦ/dt, where N is the number of turns in the loop (assuming N = 1 for a single loop), and dΦ/dt is the rate of change of magnetic flux. The magnetic flux Φ is given by Φ = B * A, where B is the magnetic field. Since B is changing uniformly, we can multiply the rate of change of the magnetic field by the area to find dΦ/dt.
Therefore, the induced EMF is ε = -1 * A * dB/dt = -1 * π * (0.55×10⁻¹ m)^2 * (2.0×10⁻¹ T/s). Calculating this value will give the magnitude of the induced EMF. The negative sign indicates the direction of the induced EMF according to Lenz's Law, which creates a current whose own magnetic field opposes the change in the original magnetic field.