How Does Flipping a Ring Affect Magnetic Flux and Induced EMF?

[ghostbuster25]

The Earth’s magnetic field at a certain location in the UK has a magnitude of 48 μT and is directed at 66° below the horizontal.

a)Determine the magnitude of the flux of the Earth’s magnetic field through a
wedding ring of diameter 2.2 cm when the ring is held in a horizontal plane.

b)What is the magnitude of the flux change when the ring is flipped through 180° about a horizontal axis?

c)Use Faraday’s law to calculate the EMF induced in the ring when it is flipped
through 180° in 0.2 s, assuming the flux changes uniformly during this time.


can anyone help me please i am completely stuck and don't know where to start :(

 

[Mindscrape]

You would actually probably be better off posting this in introductory physics, but that's okay, let me give you a hand anyway.

a) Remember that the equation for flux is $$\int \int \mathbf{B}\cdot d\mathbf{a}=\int \int B cos(\phi) da$$

b) You should have an intuitive guess about this, but go ahead and work it out.

c) Remember that EMF is $$\frac{d \Phi}{dt}$$

 

[cerium]

Hi ghostbuster remember the B dot A cross product rule that helped me and the angle is below thw horizontal so work out the angle you need

 

[billmcalpine7]

Not all that astonishingly, I have the same homework as ghostbuster. it's getting pretty late now though, but here are my tenuous attempts at the three questions:

a)


Magnetic flux = B dot A; this is the dot product of the B vector and the area vector, A

B = 48 x10^-6 T at 34 degrees from the normal vector to the the area

The A vector has magnitude = the area, and is directed perpendicular to the surface.
Mag A = (2.2 x 10^-2 m)^2

Therefore
flux = (48 x 10^-6 T) (Pi) [(2.2 x 10^-2 m)^2] (cos 34)
= 2.75 x 10^-6 T m ^2

(b)

The A vector changes direction

Δ flux = B A cos (156) – BA cos (34)
= ( -0.9135 - 0.8290) x 10^-8
= 1.7425 x 10^-8 T m2

[c]

Using Faraday's law

EMF = -N dΦ
dt

= -1 -1.7425 x 10-8 T m2
0.2 s

= 8.7125 x 10^-8 V

I had some help from a guy, who's reasoning I can't quite follow now he's gone. Part (a) makes most sense to me, but am rather lost with b and c. any help, or hints would be very gratefully recieved

 

[paranormal]

a) To determine the magnitude of the flux of the Earth's magnetic field through the wedding ring, we can use the formula: Φ = BAcosθ, where Φ is the magnetic flux, B is the magnetic field strength, A is the area of the ring, and θ is the angle between the magnetic field and the normal to the surface of the ring.

In this case, we have B = 48 μT, A = πr² = π(0.011 m)² = 3.8 x 10^-4 m², and θ = 66°. Plugging these values into the formula, we get Φ = (3.8 x 10^-4 m²)(48 μT)(cos 66°) = 1.58 x 10^-5 Wb.

b) When the ring is flipped through 180°, the angle between the magnetic field and the normal to the surface of the ring changes from 66° to 180°-66° = 114°. Using the same formula as above, the magnitude of the flux change is given by ΔΦ = BAΔcosθ = (3.8 x 10^-4 m²)(48 μT)(cos 114° - cos 66°) = -2.61 x 10^-5 Wb.

c) According to Faraday's law, the induced EMF is given by ε = -NΔΦ/Δt, where N is the number of turns in the ring, ΔΦ is the change in magnetic flux, and Δt is the time taken for the change to occur.

In this case, N = 1, ΔΦ = -2.61 x 10^-5 Wb (since the flux is decreasing), and Δt = 0.2 s. Plugging these values into the formula, we get ε = -(1)(-2.61 x 10^-5 Wb)/0.2 s = 1.31 x 10^-4 V.

This means that when the ring is flipped through 180° in 0.2 s, an EMF of 1.31 x 10^-4 V is induced in the ring.

I hope this helps you get started! Remember to always use the appropriate formulas and units when solving problems involving magnetic flux and EMF.