EMF induced in rotating rod inside uniform magnetic field

In summary, we have a 40 cm rod rotating at 15 rad/s in a uniform magnetic field of 6.4 T. To find the potential difference between the center and either end of the rod, we use the formula emf = -ΔΦ/Δt, where emf is the electromotive force, ΔΦ is the change in magnetic flux, and Δt is the change in time. We also use the formula ω = 2π/T to determine the time for half the rod to complete a full rotation. Finally, we use the formula emf = -Bπr^2/T to calculate the potential difference, taking into account that the rod covers
  • #1
songoku
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Homework Statement


A 40 cm rod is rotated about its centre inside a region of uniform magnetic field of 6.4 T. Given that the speed of rotation is 15 rad/s, find potential difference between the centre and either end of the rod

Homework Equations


emf = - ΔΦ / Δt

ω = 2π / T

The Attempt at a Solution


emf = - B cos θ . ΔA / Δt = - B . πr2 / T

I just need to plug the numbers with r = 20 cm (because from center to either end of rod)?

Thanks
 
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  • #2
In one full period T, the radius of the rod which is ##r=20cm## (since ##d=40cm## is the diameter) covers a surface of a full circle which is ##\pi r^2##. You can use the diameter but then you ll have to take the formula ##\pi\frac{d^2}{4}## for the surface of the circle.
 
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  • #3
Delta2 said:
In one full period T, the radius of the rod which is ##r=20cm## (since ##d=40cm## is the diameter) covers a surface of a full circle which is ##\pi r^2##. You can use the diameter but then you ll have to take the formula ##\pi\frac{d^2}{4}## for the surface of the circle.

For the time, do I use the period because half of the rod travels full circle in one full period or I use half of period because one whole rod covers one full circle in half period?

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  • #4
songoku said:
For the time, do I use the period because half of the rod travels full circle in one full period or I use half of period because one whole rod covers one full circle in half period?

Thanks
You use the full period for half rod, otherwise if you follow the 2nd approach you find the EMF between the two ends of the rod. But the problem asks for the EMF between one end and the center, that's why we have to take the area that the half rod covers in one full period.
 
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  • #5
Delta2 said:
You use the full period for half rod, otherwise if you follow the 2nd approach you find the EMF between the two ends of the rod. But the problem asks for the EMF between one end and the center, that's why we have to take the area that the half rod covers in one full period.

If the question asks the emf between two ends of the rod, will the answer be zero because they have the same value and the difference = 0?

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  • #6
songoku said:
If the question asks the emf between two ends of the rod, will the answer be zero because they have the same value and the difference = 0?

Thanks
Yes, the emf between the two ends is zero.
 
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  • #7
Thank you very much
 
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Related to EMF induced in rotating rod inside uniform magnetic field

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

EMF (electromotive force) is the voltage generated in a conductor when it moves through a magnetic field. In the case of a rotating rod inside a uniform magnetic field, the EMF induced is due to the changing magnetic flux through the rod as it rotates.

2. How is the direction of the induced EMF determined?

The direction of the induced EMF is determined by the right-hand rule. If the thumb of your right hand points in the direction of the rod's rotation, and your fingers point in the direction of the magnetic field, then the direction of the induced EMF will be perpendicular to both your thumb and fingers.

3. What factors affect the magnitude of the induced EMF?

The magnitude of the induced EMF depends on the strength of the magnetic field, the length of the rod, the speed of rotation, and the angle between the magnetic field and the rod's axis of rotation. It also depends on the material of the rod, as different materials have different electrical conductivities.

4. How can the induced EMF be increased?

The induced EMF can be increased by increasing the strength of the magnetic field, increasing the length of the rod, increasing the speed of rotation, or increasing the angle between the magnetic field and the rod's axis of rotation. Additionally, using a material with higher electrical conductivity can also increase the induced EMF.

5. What are some real-life applications of the concept of EMF induced in a rotating rod inside a uniform magnetic field?

One common application is in generators, where mechanical energy is converted into electrical energy by rotating a coil of wire inside a magnetic field. This principle is also used in electric motors, where electrical energy is converted into mechanical energy to produce motion. Additionally, this concept is used in devices such as induction cooktops and magnetic levitation trains.

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