Electricity and Magnetism problem

[retupmoc]

Not even sure where to begin with this question:

Estimate the magnitude of the potential difference produced by the motion of a conductor in the Earth's magnetic field for which B is 4.3x10^-5T and the angle of dip (the angle it makes with the horizontal) is 60 degrees. Take as an example a car bumper of length 1.5m traveling at 100kmh-1

Another question which seems so straight forward, i attempted i couldn't get the correct answer can you point me out where I am going wrong.

A closely wound rectangular coil of 50 turns has dimensions 12cmx25cm. The plane of the coil is rotated from a position where it makes an angle of 45degrees with a magnetic field 2T to a position perpendicular to the field in a time of 0.1s. What is the average EMF induced in the coil?

i made a couple assumptions which I am not sure are correct
1. i assumed the initial angle of 45 degrees was between the area vector normal to the plane of the coil to the direction of B.
2. that the angle through which the coil moved in 0.1s was 45degrees and not 315degrees as the question is unclear on this.


Heres what i did

found the area to be 0.0375m^2
then used the equation theta=w0t+0.5(alpha)t^2

assuming no angular acceleration as we've only been dealing with constant angular motion with ssimple ac generators and using theta=pi/4 radians i get w=7.85 rad s-1.

Then got E = wNBAsinwt which i thinks right. i then worked out E(max) and divided the answer by SQRT(2) assuming the root mean square emf by average EMF. the answer should be 8.787V but I am almost double. Can you see where I am going wrong

help would be much appreciated thanks

retupmoc

 

[Doc Al]

Originally posted by retupmoc
Not even sure where to begin with this question:

Estimate the magnitude of the potential difference produced by the motion of a conductor in the Earth's magnetic field for which B is 4.3x10^-5T and the angle of dip (the angle it makes with the horizontal) is 60 degrees. Take as an example a car bumper of length 1.5m traveling at 100kmh-1

Start by figuring the direction of the magnetic force on the charge carriers in the bumper.
[tex]\vec{F} = q \vec{v} \times \vec{B}[/tex]
Only the component along the length of the bumper (which is horizontal) contributes to the emf.

Another question which seems so straight forward, i attempted i couldn't get the correct answer can you point me out where I am going wrong.

...
i made a couple assumptions which I am not sure are correct
1. i assumed the initial angle of 45 degrees was between the area vector normal to the plane of the coil to the direction of B.
2. that the angle through which the coil moved in 0.1s was 45degrees and not 315degrees as the question is unclear on this.

Looks good to me.

Heres what i did

found the area to be 0.0375m^2
then used the equation theta=w0t+0.5(alpha)t^2

First, that area is wrong I think. More importantly, I think your approach is more complicated than needed. To find the average emf just find the change in flux divided by the time.

 

[M98Ranger]

It seems like you are on the right track with your calculations, but there are a few things that may be causing your incorrect answer.

Firstly, for the first problem, you are correct in assuming that the initial angle of 45 degrees is between the area vector normal to the plane of the coil and the direction of the magnetic field. This is important because it determines the angle at which the coil will move through the magnetic field.

Secondly, for the second problem, you are correct in assuming that the coil moves through a total angle of 45 degrees in 0.1 seconds. This can be determined by using the equation v = ωr, where v is the linear velocity of the coil, ω is the angular velocity, and r is the radius of the coil (in this case, half the length of the longer side of the rectangle).

However, there may be some errors in your calculations. For the first problem, you should use the equation V = Bvl, where V is the potential difference, B is the magnetic field strength, v is the linear velocity of the conductor, and l is the length of the conductor moving through the magnetic field. In this case, the length of the car bumper is given as 1.5m, and the velocity is given as 100 km/h, which should be converted to m/s before plugging into the equation.

For the second problem, you should use the equation E = NABωsinθ, where E is the induced EMF, N is the number of turns in the coil, A is the area of the coil, B is the magnetic field strength, ω is the angular velocity, and θ is the angle between the area vector and the magnetic field. In this case, the area of the coil is given as 0.0375m^2, and the angular velocity can be calculated using the equation ω = θ/t, where t is the time it takes for the coil to rotate through the given angle.

Double check your calculations and make sure you are using the correct equations and units. If you are still having trouble, try breaking down the problem into smaller steps and double check each step to make sure it is correct. Good luck!