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

-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 = 3.141x10⁻² 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 = 7.854x10⁻⁴ T. m²

ξ = - NΔΦ/Δt

ξ = - (1*7.854x10⁻⁴) / 0.0250

ξ = - 3.141x10⁻² V

The negative sign is due to Lenz law.