A circular loop of wire with a radius of 4.0 cm is in a uniform magnetic field of magnitude 0.069 T. The plane of the loop is perpendicular to the direction of the magnetic field. In a time interval of 0.40 s, the magnetic field changes to the opposite direction with a magnitude of 0.043 T. What is the magnitude of the average emf induced in the loop?

Given Information:  

Radius of circular loop = r = 4 cm = 0.04 m

Initial Magnetic field = B₁ = 0.069 T

Final Magnetic field = B₂ = 0.043 T

time interval = Δt = 0.40 seconds

Required Information:  

Average induced emf = ξ = ?  

Average induced emf = 3.26x10⁻⁴ V

Explanation:  

The induced EMF ξ is given by  

ξ = -NΔΦ/Δt  

Where change in flux ΔΦ can be found using

ΔΦ = (B₂ - B₁)A

Area is given by

A = πr²

A = π(0.04)²

A = 0.005026 m²

ΔΦ = (0.043 - 0.069)* 0.005026

ΔΦ = -0.0001306 T.m²

So the average induced emf is

Assuming number of turns N = 1

ξ = -NΔΦ/Δt

ξ =   -1*(-0.0001306)/0.40

ξ = 0.0003265 V

ξ = 3.26x10⁻⁴ V

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