Potential of a rod moving through electric field

[lennardivoodo]

Homework Statement

A vertical wire with current I, and a rod, perpendicular to the wire, at a distance d from the wire and with a length of L. The rod is moving with velocity v parallel to the wire. What is the potential at the far end of the rod given the chosen potential at the end of the rod closest to the wire is zero.

Homework Equations

B=\epsilon*I*(2*pi*L)
V=E

The Attempt at a Solution

So I started with trying to find the overall magnetic field the rod goes through, by integrating B from d to d+L, leaving me with ln((d+L)/d)*ϵ0*I/(2*pi)
Then given E=Electric potential, emf=E*L,
B*v=E=V

V=v*ln((d+L)/d)*ϵ0*I/(2*pi)

I doubt this is correct though, any help would be greatly appreciated.

 

[anathema]

Hi there,

Your approach seems to be on the right track, but there are a few things that need clarification and correction.

Firstly, the equation B = ε0*I*(2*pi*L) is not applicable in this situation. This equation is used for calculating the magnetic field at the center of a circular loop of wire, not for a wire and a rod configuration.

Instead, you can use the Biot-Savart law to calculate the magnetic field at a point P due to a current-carrying wire. The equation is given by:

B = (μ0*I)/(2*pi*r)

where μ0 is the permeability of free space, I is the current in the wire, and r is the distance between the wire and the point P.

Next, you need to find the magnetic field at the far end of the rod. To do this, you can use the superposition principle, which states that the total magnetic field at a point due to multiple sources is the vector sum of the individual magnetic fields at that point.

So, the magnetic field at the far end of the rod will be the sum of the magnetic field due to the wire and the magnetic field due to the moving rod. You can use the Biot-Savart law to calculate the magnetic field due to the wire, and you can use the Lorentz force law to calculate the magnetic field due to the moving rod.

Once you have the magnetic field at the far end of the rod, you can use the equation V = B*v to calculate the potential at that point.

I hope this helps! Let me know if you have any further questions.