A single-turn circular loop of wire of radius 5.0 cm lies in a plane perpendicular to a spatially uniform magnetic field. During a 0.02500.0250-\text{s}s time interval, the magnitude of the field increases uniformly from 200 to 300 mT. Determine the magnitude of the emf induced in the loop
Question
Answer:
-0.0314 V
Explanation:
Parameters given:
Initial magnetic field, Bini = 200 mT = 0.2T
Final magnetic field, Bfin = 300mT = 0.3 T
Number of turns, N = 1
Radius, r = 5 cm = 0.05 m
Time, t = 0.025 secs
Induced EMF is given as:
EMF = [-(Bfin – Bini) * N * pi * r²] / t
EMF = [-(0.3 – 0.2) * 1 * 3.142 * 0.05²] / 0.025
EMF = (-0.1 * 3.142 * 0.0025) / 0.025
EMF = -0.0314 V
Given Information:
time = Δt = 0.0250 seconds
Radius = r = 5 cm = 0.05 m
Change in Magnetic field = ΔB = (0.300 – 0.200) T
Number of turns = N = 1
Required Information:
Magnitude of induced emf = ξ = ?
Answer:
Magnitude of induced emf = ξ = 3.141×10⁻² V
Explanation:
The EMF induced in a circular loop of wire in a changing magnetic field is given by
ξ = -NΔΦ/Δt
Where change in flux ΔΦ is given by
ΔΦ = ΔBA
ΔΦ = ΔBπr²
ΔΦ = (0.300 – 0.200)*π*(0.05)²
ΔΦ = 7.854×10⁻⁴ T.m²
ξ = -NΔΦ/Δt
ξ = -(1*7.854×10⁻⁴)/0.0250
ξ = -3.141×10⁻² V
The negative sign is due to Lenz law.