How Is Average Voltage Calculated in a Changing Magnetic Field?

[wayneinsane]

Homework Statement

There is uniform magnetic field of 25 mT into paper in a region.
Where there is kink in a wire..

The initial diameter of the kink is 2 cm. The wire is pulled out and kink shrinks to dosimeter = 0 in 50 ms.

(i) Determine the average voltage between A and B. and the polarity of A and B.

(ii) Suppose the kink is undisturbed and the magnetic field increases to 100 mT in 4 x 10-3 s, then determine the average voltage between A and B and the polarity of A and B.

Homework Equations

magnetic flux = BAcos(theta)

emf = -N magnetic flux / delta T

The Attempt at a Solution

for (i), I did magnetic flux = BAcos(theta)... B = 2.5x10^-2 T, A = 3.14x10^-4, and cos theta = 1... so mag flux = 7.85x10^-6...so plug that into emf and you get 7.85x10^-6/50x10^-3s and you get 1.57x10^-4V...is this correct??

for (ii) i did change in flux so Bf x A - Bi x A which is 5.14x10^-5 T - 7.85 x 10^-6 T which gives 2.355 x 10^-5T... you plug that into EMF equation and get 2.355x10^-5T/4x10^-3s which equals 5.89x10^-3V...is this correct??

 

[anathema]

Hello! Your calculations seem to be correct. The average voltage between A and B in the first scenario would be 1.57x10^-4V and the polarity would be positive at A and negative at B. In the second scenario, the average voltage between A and B would be 5.89x10^-3V and the polarity would be positive at A and negative at B. Great job!

 

[nlightner]

I can confirm that your calculations for the average voltage between A and B in both cases are correct. However, it is important to note that the polarity of A and B cannot be determined without knowing the direction of the current flow. The polarity will depend on whether the current is flowing from A to B or from B to A. Additionally, it is important to use consistent units in your calculations. In the first case, you used meters for the magnetic field, but in the second case, you used Tesla. It is important to use the same unit throughout the calculation to avoid errors. Overall, your approach and calculations are correct, but it would be helpful to include more information about the direction of the current in order to determine the polarity of A and B.