# conservation of flux

Discussion in 'Homework Help' started by elecidiot, Feb 11, 2011.

1. ### elecidiot Thread Starter New Member

Jun 29, 2010
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Hi I just want to know what is meant by conservation of magnetic flux or continuity of magnetic flux in electric circuits. What is its significance. Where and how is it is helpful in circuit analysis?. I can understand the concept of charge conservation in case of capacitors stating that the initial charge in a network of capacitors is same as that of the final charge in the capacitor network(even this holds true under certain conditions I presume) but regarding inductors I surely have no idea. Please help.

2. ### Georacer Moderator

Nov 25, 2009
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1,266
Both capacitor and inductor networks support the principle of energy conservation, in their version each.

In a capacitor network the expression is something like that:
Initial Energy Source=Sum of Initial Capacitor Charges
Final Energy Source=Sum of Final Capacitor Charges
Losses=Heat dissipation on the network resistors.

Which gives us:
Initial Energy=Final Energy + Losses

In an inductor network you can think of the energy source as the current that flows through the inductors, and reform the above expressions.

Remember that in a capacitor energy is $E=\frac12 C \cdot V^2$
and in an inductor $E=\frac12 L \cdot I^2$

As for the continuity of magnetic flux, it is interpreted as follows: The current through an inductor cannot change its magnitude instantaneously. That means that if in a time moment $t_-$ the current in an inductor is $I_t$, then in the moment $t_+$ the current must be $I_t$.

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3. ### t_n_k AAC Fanatic!

Mar 6, 2009
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Another simplistic perspective based on duality .....

Consider a capacitor C initially charged to a voltage E0 and then discharged through a resistance R

The classic discharge equation is

$v_C(t)=E_0 e^{-\frac{t}{RC}}$

And the corresponding discharge current is

$i_C(t)=\frac{E_0}{R} e^{-\frac{t}{RC}}$

If one integrates the function iC(t) over the limits 0 to ∞ we obtain the simple product (independent of the value of R)

$E_0*C$

which we normally call the initial charge Q0, expressed in Coulomb. We accept without contradiction (and therefore by convention) that this charge cannot be destroyed - or rather it is always conserved.

Consider now the case of an inductor initially "charged" with a current I0 which is then discharged through a resistor R.

We obtain similar functions for the voltage and current discharge

$v_L(t)=I_0Re^{-\frac{Rt}{L}}$

$i_L(t)=I_0e^{-\frac{Rt}{L}}$

Integration of the voltage function vL(t) over the interval 0 to ∞ yields the simple product (independent of the value of R)

$I_0*L$

which we call the initial flux linkage λ0. We are not generally familiar with this term and its quantitative value with respect to its persistence. Is it like electrostatic charge with regard to conservation? Presumably yes - at least from the argument of duality. We can assign it units - In the SI system it would be the Weber.

I suspect the doubt expressed by 'elecidiot' is a result of lack of familiarity with concepts rather than any deeper or fundamental objections.

4. ### elecidiot Thread Starter New Member

Jun 29, 2010
23
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I agree with t_n_k. I am now only beginning to learn the concepts. So only so many questions are being raised. I hope wizards like t_n_k and georacer will provide constructive criticism and help me learn. Thank u guys

5. ### Georacer Moderator

Nov 25, 2009
5,151
1,266
A wizard? I wish I was. Then I could telekinetically reach the remote of my tv...