MHB Physics: Calculate Emf, Electric Field in Magnetic Field

[Fermat1]

1)A meter long metal rod of mass m is falling with a constant velocity of 10 m/s. The rod is attached to two conducting rails. Determine the emf if there is a uniform magnetic field directed perpendicular to the motion of the bar. The resistance has a value of 105 ohms.

I don't know how I can do it when the magnetic field is not given

2)A loop of wire is put in a changing magnetic field. The magnetic flux through the loop is given by $4t(t+2)$. The loop is connected to a parallel plate capacitor that has a plate separation of 15mm. Determine the electic field between the plates at time $t=3$ s.

Can I assume that potential difference equal emf if the wire has no resistance?

3)Let $V=(xyt^3T)i+(x^4tT)j$. Find the curl of the magnetic field and the electric field. I've found the curl.
The curl I found to be $-(4x^3t)j+(yt^3)k$ It's sensible to leave out the units T right?

How do I find the electric field?

 

[I like Serena]

1)A meter long metal rod of mass m is falling with a constant velocity of 10 m/s. The rod is attached to two conducting rails. Determine the emf if there is a uniform magnetic field directed perpendicular to the motion of the bar. The resistance has a value of 105 ohms.

I don't know how I can do it when the magnetic field is not given

It seems to me that if there is no current in the bar, and if there is not change in flux, there won't be an emf.

2)A loop of wire is put in a changing magnetic field. The magnetic flux through the loop is given by $4t(t+2)$. The loop is connected to a parallel plate capacitor that has a plate separation of 15mm. Determine the electic field between the plates at time $t=3$ s.

Can I assume that potential difference equal emf if the wire has no resistance?

That is what I would assume with no more information given.

3)Let $V=(xyt^3T)i+(x^4tT)j$. Find the curl of the magnetic field and the electric field. I've found the curl.
The curl I found to be $-(4x^3t)j+(yt^3)k$ It's sensible to leave out the units T right?

How do I find the electric field?

Since the formula for $V$ contains the unit T, it makes sense to also specify it in an answer. Anyway, since it is an SI unit, it won't hurt much to leave it out.

How did you find the curl of the magnetic field?

And what is being asked exactly? The electric field? Or the curl of the electric field?

 

[topsquark]

1)A meter long metal rod of mass m is falling with a constant velocity of 10 m/s. The rod is attached to two conducting rails. Determine the emf if there is a uniform magnetic field directed perpendicular to the motion of the bar. The resistance has a value of 105 ohms.

I don't know how I can do it when the magnetic field is not given

Lenz's Law says that if the flux through the loop is changing then there will be a force to counteract the changing flux. In this case we know that the rod is falling with a constant speed...that is to say that there must be a force on the rod, equal to the weight of the rod, in the upward direction. What does that tell you about the magnetic field?

-Dan

 

[jacobi1]

It seems to me that if there is no current in the bar, and if there is not change in flux, there won't be an emf.

There is a current in the bar-otherwise the bar will accelerate as it falls.
The magnetic force is given by [math]iL \times B[/math], where i is current, L is the bar's length, and B is the magnetic field. The magnetic field is perpendicular to the motion, so the magnitude, [math] iLB \sin \theta [/math], becomes [math]iLB[/math], and the direction, by the right-hand rule, is opposite to the direction of the gravitational force. Since the bar falls with constant velocity, this force is equal in magnitude to the gravitational force. Thus [math] iLB=mg[/math].
But [math] i= \frac{\epsilon}{R} [/math], where [math]\epsilon[/math] is emf. So, Fermat, what do you think you should do now?
Faraday's law, maybe?