A circular loop of radius 25 cm is sitting in a perpendicular magnetic field of 0.2 T. If the magnetic field strength remains the same value of 0.2 T, calculate the induced EMF in the loop.
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To calculate the induced EMF (electromotive force) in the loop, we can use Faraday's Law of electromagnetic induction, which states that the induced EMF is equal to the rate of change of magnetic flux through the loop.
The magnetic flux through a loop is given by the product of the magnetic field strength (B) and the area (A) of the loop, i.e., Φ = B * A.
In this case, the loop is circular with a radius of 25 cm, so its area (A) can be calculated using the formula A = π * r^2, where r is the radius of the loop.
Given that the radius of the loop is 25 cm, we need to convert it to meters to maintain consistent units in the calculations. Hence, r = 25 cm = 0.25 m.
Therefore, the area of the circular loop is A = π * (0.25)^2 = π * 0.0625 = 0.19634954 m^2 (approx.)
Now, we can calculate the magnetic flux (Φ) through the loop by multiplying the magnetic field strength (B) with the area of the loop (A). In this case, B = 0.2 T.
Φ = B * A = 0.2 T * 0.19634954 m^2 ≈ 0.03926991 Tm^2
Finally, the induced EMF (ε) in the loop can be calculated by taking the derivative (rate of change) of the magnetic flux with respect to time (t).
ε = dΦ/dt
However, since the problem states that the magnetic field strength remains constant at 0.2 T and does not mention any changes in time, we can assume that the induced EMF is zero in this scenario.