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

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 = ?  

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.

its a 5.5 n

glad that