Answer to Question #107213 in Electricity and Magnetism for Vitezslav Havelek

Question

We have a conductor outside homogeneous magnetic field. The length of a conductor is 1m, the strength of magnetic field 1T. We measure emf voltage at the ends of a conductor. Now we will push the conductor inside a magnetic field bz speed 1m/s parpendicullary, so we will start measure voltage 1V.
The question is how fast the voltage will increase to its maximum 1V. I know the time will be very small but it will not be definitely zero. What will be the curve of increasing voltage and is it constant or it will depend on a speed, magnetic field strength or conductor length in any way? This is essential for my simulator I am working on, which works with speed of the light resolution so even inter-electrons relations should be solved in detail...

Answer 1

In short, then

(1) a conductor begins to move in the magnetic field

$E=\frac{d\Phi}{dt}=-\frac{B(dS\cdot l)}{dt}=-Bv_0l (v_0=const)$. It is clear. But when $t=0$ then $v=0$ ,

and $t=\tau$ then $v=v_0$. That is $v=at\to t\approx\frac{v}{a}.$.

(2) a conductor outside homogeneous magnetic field. In this case based on classic ideas I got (for wire 1 mm x 1 mm)

$U\approx \frac{q\cdot n\cdot x\cdot v\cdot t}{4\pi\epsilon_0}\to t\approx 8\cdot10^{-18} s$

where

q - the charge of electron;

n - the concentration of electrons in the conductor;

x - thickness of the conductor (I assumed that the conductor was rectangular and made of copper).