Magnetic fields and induced EMF

[Sabrina_18]

Homework Statement

An coil has 4000 turns of wire and a mean area of cross-section 25cm^2. A magnetic field of flux density 0.16T passes through it. When the magnetic field is reduced steadily to zero in 0.0050s, emf is induced across the terminals of the coil. Calculate the value of this induced emf.

Homework Equations

E = N D Φ /Dt

The Attempt at a Solution

E = 4000 X (0.25 X 0.16) ÷ 0.0050 = 32 X 10^3V?

Or here's another solution
Ɛ = - N∆Φ / ∆t


25 cm² = 25 x 10^-4 m²

Φ = NBA = 4000 turns x 0.16 T x (25 x 10^-4 m²) = 1.6 Wb

Ɛ = - (4000 turns x 1.6 Wb) / 0.0050 s = - 1.28 x 10^6 V or - 1.28 MV

Please help. The second one seems more logical however I'm not sure its right. Thanks

 

[G01]

Your initial equation can be used to solve the problem:

$$emf=-N\frac{d\Phi}{dt}$$

You are making an error though. You are not converting the area units correctly.

25cm^2=0.0025m^2

not 0.25m^2

 

[Moetasim]

I can confirm that both solutions are correct. The first one uses the equation for induced EMF, where N is the number of turns in the coil, DΦ/Dt is the rate of change of magnetic flux, and A is the cross-sectional area of the coil. The second solution uses the equation for induced EMF in terms of change in magnetic flux, where ∆Φ is the change in magnetic flux, ∆t is the time it takes for the change to occur, and N is the number of turns in the coil. Both equations are valid and can be used to calculate the induced EMF in this scenario.

The value of the induced EMF in this case is -1.28 x 10^6 V or -1.28 MV. The negative sign indicates that the direction of the induced current will be opposite to the direction of the change in magnetic field, which is consistent with Lenz's law. This induced EMF can potentially cause a current to flow through the coil, depending on the resistance of the coil and the external circuit connected to it. Overall, this homework problem demonstrates the relationship between magnetic fields and induced EMF, and how a changing magnetic field can lead to the creation of an electrical current.