Induced EMF in Rotating Magnetic Field with B=0.5B0z^

In summary, the induced emf can be calculated using the formula d(flux)/dt = 0.5B0*pi*r^2*-sinq(t)*dq(t)/dt, where B is the magnetic field of 0.5B0z^, r is the radius of the loop, and w is the angular velocity of rotation. The angle q is needed to fully calculate the induced emf, which can be found by evaluating the flux using the formula phi = Bcosq(t)SdA. The integration sign, S, was mistakenly included in the previous equations.
  • #1
assaftolko
171
0
A magnetic field of B=0.5B0z^ is present when a loop with radius r is rotated around the y-axis with angular velocity of w=9 rad/s. What is the induced emf?

Well: flux = SB*dA = SBdAcosq(t) = Bcosq(t)SdA = 0.5B0*pi*r^2cosq(t)

d(flux)/dt = 0.5B0*pi*r^2*-sinq(t)*dq(t)/dt = 0.5B0*pi*r^2*-sinq(t)*9.

But I'm still stuck with the angle q which isn't given to me... What should I do?
 

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  • #2
assaftolko said:
A magnetic field of B=0.5B0z^ is present when a loop with radius r is rotated around the y-axis with angular velocity of w=9 rad/s. What is the induced emf?

Well: flux = SB*dA = SBdAcosq(t) = Bcosq(t)SdA = 0.5B0*pi*r^2cosq(t)

d(flux)/dt = 0.5B0*pi*r^2*-sinq(t)*dq(t)/dt = 0.5B0*pi*r^2*-sinq(t)*9.

But I'm still stuck with the angle q which isn't given to me... What should I do?

The attachment shows ##B=(1/2)B_0 t^2## and you use ##B=(1/2)B_0##.

And what is S?
 
  • #3
I think you are mostly correct. However, what should the argument of cosq(t) be? could it be cosq(9t)?
 
  • #4
The first magnetic field is from another part of the question - if you look at the bottom you'll see the field I wrote here. S in the sign of integration ∫, forgot about the operators here :P
 
  • #5
barryj said:
I think you are mostly correct. However, what should the argument of cosq(t) be? could it be cosq(9t)?

You're right! It's analoug to x=vt for constant speed movement... thanks!
 
  • #6
assaftolko said:
The first magnetic field is from another part of the question - if you look at the bottom you'll see the field I wrote here. S in the sign of integration ∫, forgot about the operators here :P

Ah ok but I don't think you need to deal with integrals here.

You know ##\phi=\vec{B}.\vec{A}##. The direction of A is perpendicular to plane of ring. When the area vector rotates by an angle ##\theta##, evaluate ##\phi##.

PS: Can you post the answer so that I can check my working?
 

1. What is induced EMF in a rotating magnetic field?

Induced EMF (electromotive force) refers to the voltage generated in a conductor when it is exposed to a changing magnetic field. In a rotating magnetic field, the magnetic field is constantly changing in direction, which results in an induced EMF.

2. How is the strength of induced EMF determined in a rotating magnetic field?

The strength of induced EMF in a rotating magnetic field is determined by the strength of the magnetic field (B), the speed of rotation, and the angle between the magnetic field and the conductor (θ). It can be calculated using the formula: EMF = Bωl sin(θ), where ω is the angular velocity and l is the length of the conductor.

3. What is the direction of induced EMF in a rotating magnetic field?

The direction of induced EMF in a rotating magnetic field is determined by Lenz's law, which states that the induced current will flow in such a direction as to oppose the change in magnetic field that produced it. This means that the direction of the induced EMF will be opposite to the direction of the changing magnetic field.

4. How does the strength of the magnetic field affect the induced EMF in a rotating magnetic field?

The strength of the magnetic field (B) directly affects the strength of the induced EMF. As the magnetic field increases, the induced EMF also increases. This is because a stronger magnetic field will result in a greater change in flux over time, leading to a larger induced EMF.

5. What is the relationship between the frequency of rotation and the induced EMF in a rotating magnetic field?

The frequency of rotation has a direct relationship with the induced EMF in a rotating magnetic field. As the frequency of rotation increases, the induced EMF also increases. This is because a higher frequency means the changes in the magnetic field are happening at a faster rate, leading to a larger induced EMF.

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