RC circuit + magnetic induction (B field)

A capacitor has been charged to $V_o$ , a metal bar with mass m ,resistor R is located between two parallel wire (distance L) in magnetic field B, as shown in the above figure.
At t=0; the switch was turn from a to b.
Current I will flow throught metal bar, which F=I L B will accelerate meta bar. $m\frac{dv}{dt}=I L B$ .
When the metal bar is moving, the changing in magnetic flux will induce voltage $V_i= B L v$
So the equation for the loop is $Vc= \frac{Q_c}{C} = I R + B L v$ , where $I=-\frac{dQ_c}{dt}$

$\frac{1}{C} \frac{dQ_c}{dt}=-I =R \frac{dI}{dt}+B L \frac{dv}{dt}= R \frac{dI}{dt}+B L \frac{BLI}{m}$
, $\frac{dI}{dt}=-(\frac{1}{RC}+\frac{B^2L^2}{mR}) I$
the solution is $I(t)=\frac{V_o}{R}(1-e^{-\alpha t})$ ,where $\alpha=\frac{1}{RC}+\frac{B^2L^2}{mR}$

The following is a simulation for the above case:
The charge $Q_c(t)$ , the velocity $v(t)$ and the current $I(t)$ are shown (C=1 in the calculation).

Press the Alt key and the left mouse button to drag the applet off the browser and onto the desktop.
This work is licensed under a Creative Commons Attribution 2.5 Taiwan License

Please feel free to post your ideas about how to use the simulation for better teaching and learning.
Post questions to be asked to help students to think, to explore.
Upload worksheets as attached files to share with more users.

Let's work together. We can help more users understand physics conceptually and enjoy the fun of learning physics!

Related Topics
	Subject	Started by	Replies	Views	Last post
	Electron in magnetic field Electromagnetism	Fu-Kwun Hwang	10	23977	September 11, 2009, 02:40:41 PM by Fu-Kwun Hwang
	Magnetic field generated bar magnet Electromagnetism	Fu-Kwun Hwang	4	7759	September 28, 2009, 09:00:19 AM by lookang
	magnetic induction communication system Electromagnetics	Taona	5	3106	May 04, 2009, 12:38:50 AM by Taona
	Individual and Resultant Force Magnetic Field of a wire and external mag. field Request for physics Simulations	lookang	8	4101	December 10, 2009, 10:42:37 PM by Fu-Kwun Hwang
	RC circuit + magnetic induction (B field) electromagnetism	ahmedelshfie	0	209	May 25, 2010, 06:48:45 PM by ahmedelshfie

	Author	Topic: RC circuit + magnetic induction (B field) (Read 2206 times)
0 Members and 1 Guest are viewing this topic. Click to toggle author information(expand message area).