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?

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

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