Question

a circular conducting loop with radius of 0.024 m is in a uniform, 3.0-t magnetic field that is normal to the plane of the loop (directed outward as shown). what is the magnitude of the average induced emf in the loop if it is pulled out of the region of the field in 0.2 s (without changing its orientation relative to the field direction)? note: the area of the non-circular portion of the wire is negligible compared to that of the circular loop and should be ignored.

Answer 1

Using faraday’s law:
ε=-N ΔΦ/ΔT
ε=-N Δ(ABcosθ)/ΔT
In this question the magnetic field is changing so
ε=-NAcosθ (Bf - Bi)/ΔT
Since the orientation does not change we can remove cosθ
ε=-NA (Bf - Bi)/ΔT
Now let’s write our givens
N=1 (it’s just a circular loop)
A (of a circle) = π * (0.024)^2 = 5.8π x 10^-4 m^2
Bf = 0 T (because the loop is pulled out)
Bi = 3 T
ΔT = 0.2
Now let’s substitute
ε=-(1)(5.4π x 10^-4) (0-3)/0.2
Use a calculator
ε=0.027 V

Hope this helps