 #1
JoelKTH
 16
 1
 Homework Statement:

A homogenous Bfield B= B e_x + B e_z is acting in space. A metalbar is attached in a horisontal axis, mounted on the height y=L on the yaxis. The metal bar is swinging freely in the xyplane around the axis. The metal bars pendulummovement is described as α(t) = β cos(ωt) which is time dependent on t. β > 0 och ω > 0 are constants. The metal bar lower end is in electrical contact with a metal rail with the geometry of a circular arc with radius L. The metal bar is through the resistance R coupled to the axis and the bar as the figure shows. The the selfinductance of the circuit is being neglected as the circuits other resitive losses.
Calculate the current i(t) and use Lenz law to validate that the currents sign is correct.
 Relevant Equations:
 emk=  d(phi)/dt, i(t)= emk/R, phi=surface integral(B dS)
Hi, the problem statement is above. I have some questions about how to calculate the area and the direction of the magnetic field of this problem.
As the magnetic flux, my professor have defined it as Phi= integral(B dS)=(Area)e_x B= (Area_triangle + (L^2/2) *(β + α(t)))*B e_z.
How can one know that the magnetic field is in the e_z direction? As far as I know the right hand rule makes the direction of the magnetic field in e_phi direction. However to convert this e_phi=e_x sin(phi) + e_y cos(phi) does not help me.
Another question is how the Area is calculated. There is a figure attached. As the figure is time dependent, I am aware that the Area_triangle will change.
Kind regards,
As the magnetic flux, my professor have defined it as Phi= integral(B dS)=(Area)e_x B= (Area_triangle + (L^2/2) *(β + α(t)))*B e_z.
How can one know that the magnetic field is in the e_z direction? As far as I know the right hand rule makes the direction of the magnetic field in e_phi direction. However to convert this e_phi=e_x sin(phi) + e_y cos(phi) does not help me.
Another question is how the Area is calculated. There is a figure attached. As the figure is time dependent, I am aware that the Area_triangle will change.
Kind regards,