Answer:
(a) The induced emf is 0.162 mV
(b) The induced emf is 0.2835 mV
Explanation:
Given;
radius of the circular region, r = 1.90 mm = 1.9 x 10⁻³ m
[tex]emf = \frac{d \phi}{dt}[/tex]
ΔΦ = ΔBA
where;
ΔΦ is change in magnetic flux
ΔB is the change in the strength of magnetic field
A is the area of the circular region
Area of the circular region:
A = πr² = π (1.9 x 10⁻³)² = 1.134 x 10⁻⁵ m²
Part (a) the average induced emf around the border of the circular region
[tex]emf = \frac{d \phi}{dt} = \frac{BA}{t} = \frac{1.5*1.134*10^{-5}}{105*10^{-3}} \\\\emf = 0.162 \ mV[/tex]
Part (b) the average induced emf around the border of the circular region
initial magnetic field strength, B₁ = 1.50 T
final magnetic field strength, B₂ = 0.500 T
Change in magnetic strength, ΔB = 0.5 - 1.5 = - 1 T
initial time period, t₁ = 105 ms
final time period, t₂ = 65 ms
Change in time period, Δt = 65 - 105 = - 40 ms
[tex]emf = \frac{d \phi}{dt} = \frac{dBA}{dt} = \frac{-1*1.134*10^{-5}}{-40*10^{-3}} \\\\emf = 0.2835 \ mV[/tex]
