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JoelKTH

- 29

- 1

- Homework Statement
- A homogenous B-field 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 y-axis. The metal bar is swinging freely in the xy-plane 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 self-inductance 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(

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**d**S**)=(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__As far as I know the right hand rule makes the direction of the magnetic field in**e_z**direction?**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,