EMF induced in rotating rod inside uniform magnetic field

[songoku]

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

 

[Delta2]

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.

 

[songoku]

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?

Thanks

 

[Delta2]

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.

 

[songoku]

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?

Thanks

 

[Delta2]

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.

 

[songoku]

Thank you very much