HELP Induced Voltage question

[Trista]

HELP! Induced Voltage question

Here it is: Coil has 10 turns and shaped in an elipse (A = pie ab), having a major axis of 10 cm (10 X 10^-2 m) and minor axis 4 cm (4 X 10^-2m). Coil rotates 100 rpm in a region in which the magnitude of the Earth's magnetic field is 55 microT. What is max voltage induced in the coil if the axis of rotation of the coil is along its major axis and aligned
a) Perpendicular to Earth's magnetic field or
b) parallel

So, I figure my equation should be Emax = NBA omega sin omega t

Then, I figure my area to be: A = pi ((10 X 4)x10^-2 m^2)) = 1.26 m^2
and Omega = 2 pi(rpm / 60) -> 2 pi (100 / 60) = 10.47 rad/s

My equation then looks like this:
10(55X10^-6 T)(1.26 m^2)10.47 rad/s sin 10.47 rad/s t
But it doesn't come out right AND I don't know what t would be, as its not mentioned. a) is supposed to be 18.1 micro V and b) is 0, I suppose becuase it is parallel, no magnetic field is hitting it when parallel, right?

 

[Trista]

hahhaahaha, I got it... I needed to fix my area. S/B (4 cm / 2)(10 cm / 2) = 10 cm... got my answer, thanks anyway

 

[kyle8921]

Hello,

Thank you for your question. It seems like you are on the right track in terms of using the equation Emax = NBAωsinωt to calculate the maximum induced voltage in the coil. However, there are a few things to consider in order to get the correct answer.

First, make sure to convert all units to SI units before plugging them into the equation. This means converting the coil's major and minor axis measurements from centimeters to meters, and the Earth's magnetic field strength from microTesla to Tesla.

Second, for part a) where the coil is perpendicular to the Earth's magnetic field, the angle between the coil's axis of rotation and the magnetic field should be 90 degrees. This means that the sinωt term in the equation would become sin(90 degrees) = 1. This will give you the correct answer of 18.1 microvolts.

For part b) where the coil is parallel to the magnetic field, the angle between the coil's axis of rotation and the magnetic field should be 0 degrees. This means that the sinωt term in the equation would become sin(0 degrees) = 0. This will give you the correct answer of 0 microvolts.

Lastly, the t in the equation represents time, which is not given in the question. This is because the induced voltage in the coil will vary over time as it rotates. In order to calculate the maximum voltage, you would need to take the derivative of the equation with respect to time and set it equal to 0. This will give you the time at which the maximum voltage occurs. Alternatively, you can use a graphing calculator or software to plot the equation and find the maximum value.

I hope this helps clarify the problem and how to approach it. Good luck!