A flat, circular loop of radius r = 1 m is at rest in a uniform magnetic field of magnitude b. The plane of the loop is parallel to the page and the magnetic field is directed perpendicular to and out of the page, as indicated by the blue dots. If the magnitude of the magnetic field decreases from 8 t to 2 t in 2 s, what is the rate of change in the magnetic flux through the circular loop?.

Question

10-11-2022
Physics

Answered

A flat, circular loop of radius r = 1 m is at rest in a uniform magnetic field of magnitude b. The plane of the loop is parallel to the page and the magnetic field is directed perpendicular to and out of the page, as indicated by the blue dots. If the magnitude of the magnetic field decreases from 8 t to 2 t in 2 s, what is the rate of change in the magnetic flux through the circular loop?.

Answer :

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ikarikayah ikarikayah · Answer 1 · 2022-11-17T02:22:45-05:00

The rate of change in the magnetic flux for the induced emf in a loop is 9.42 volts.

Magnetic flux is the number of lines of force that penetrate a plane surface perpendicularly. Meanwhile, the induced emf is the emergence of an emf on the ends of the coil caused by a change in the magnetic flux enclosed by the coil.

ε = (dΦ/dt)

With:

ε = induced emf (volts)

ΔΦ = change in magnetic flux (Wb)

Δt = time interval for changing magnetic flux (s)

On a known matter

The radius of the circular loop: r = 1 m

Time: t = 2 s

Initial magnetic field: Bi = 2T

Final magnetic field: Bf = 8T

The expression for the induced emf in a loop is:

ε = (dΦ/DT) → Φ = magnetic flux

ε = [tex]\frac{d(BA cos 0)}{dt}[/tex] → θ = 90°

ε = [tex]A\frac{d(B)}{dt}[/tex]

ε = [tex]A \frac{Bf -Bi}{t}[/tex]

ε = π(1)² x (8-2/2)

ε = 22/7 x 3

ε = 9.42 volts

So, the induced emf in the loop is 9.42 volts.

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