Question

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?

Answer 1

Answer:

0.33 mV or 0.00033 V

Explanation:

Parameters given:

Radius, r = 4 cm = 0.04 m

Number of turns, N = 1

Initial magnetic field, Bini = 0.069 T

Final magnetic field, Bfin = 0.043 T

Time, t = 0.4 secs

EMF induced in a coil is given as the time rate of change of Magnetic Flux:

EMF = -ΔΦ/t

ΔΦ = ΔB * A

Where ΔB = change in magnetic field

A = area = pi * r²

EMF = -[(Bfin - Bini) * N * pi * r²] / t

EMF = -[(0.043 - 0.069) * 1 * 3.142 * 0.04²] / 0.4

EMF = 0.00033 V = 0.33 mV

Answer 2

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 = ?  

Answer:  

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