I have a variation of the Motional EMF in Tiplers Physics Second Edition 28-1. A conducting rod of mass m and lenght l sliding along conducting rails connected by a resistor with a uniform magnetic field normal to the movement of the rod. The variation is that instead of just a resistor, the cicuit also includes a hypothetical toroidal inductor of n turns per unit length and volume V= A*L that is generating the magnetic field based on the current flowing through the circuit.(adsbygoogle = window.adsbygoogle || []).push({});

assume a velocity v(0) > 0 and small initial current I(0) > 0

I want to find a function for v(t).

i started with:

a) the B = µ*n*I for the field in the gap of a toroidial solenoid.

b) the force on the wire F=I*l*B (there may need to be sin theta in there)

b.1) because of a) F=µ*I(t)^2*l*n

c) i figured that a(t)= F(t)/m

d) thinking about a small delta t v(t) = v(0) - µ*I(t)^2*l*n/m

e) i then thought about dv/dt = -(2*µ*l*n/m) * I* dI/dt

f) from LR circuits we have dI/dt= -(R/L)*I where L is the inductance which equals µ*n^2*V where V is the volume of the toroidal solenoid.

g) replacing this into the dv/dt equation i got dv/dt = -(2*µ*l*n/m) * I* (R/µ*n^2*V)*I = -(2*µ*l*R*I^2)/(n*m)

In thinking about this as an LR circuit, I began to wonder about how to account for the current source created by the combinantion of the initial current and the velocity as a source of current and began to wonder if it is possible to picture the entire circuit with the velocity and initial current as a capacitor or battery. This would help me to confirm that i could use the defintion of dI/dt that i used in f).

A secondary goal would be to use the above idea to create a circuit diagram that would allow us to create a defintion for the current over time in such a configuration.

The initial current is really to initiate the magnetic field that would then generate a current defined by B*l*v/R

any help or feed back would be appreciated!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Variation on motional emf

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**