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I have come to know from my textbook that energy is stored in the E-field of a capacitor, in the B-field of an inductor and so on. Take the example of an inductor. The derivation bewilders me completely. From Kirchhoff's Loop Rule, we take the the voltage drop along the inductor, multiply by current then integrate it wrt time to get the energy stored in an inductor. They say that the energy is stored in the B-field of inductor.

Analogically lets take the same derivation for a freely falling body opposed by drag (ohmic resistor) accelerating downwards due to g (inductor). We can find the work done by G-field and say that the gravitational potential energy of the body changes by this much. Can we say that this much energy is being stored in the gravitational-field?

In the same way the term $$\frac{1}{2} L \,i^2$$ represents the energy change of the charge flowing per unit time through the inductor. How does this relate with the energy stored in the inductor or in the B-field?

So my question, how can we define the energy stored in a force field, or at least visualise it, and why is it needed to consider that this is being stored in the field?

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  • $\begingroup$ In your analogy, the energy is stored in the gravitational field when you elevate the object. The object free-falling is like the capacitor discharging. $\endgroup$
    – glS
    Feb 3, 2015 at 8:16
  • $\begingroup$ yes, but the scenario remains the same. Energy is being released by the field. $\endgroup$
    – Sagnik
    Feb 3, 2015 at 8:21

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The energy stored in a field is the energy required to create it. In your case of the inductor there is no field when no EMF is applied. When we apply an EMF a current flows and does work, and the work goes into creating the field.

When we talk about the energy of e.g. a charge in an electrostatic field, we normally assume the charge is small enough that its effect on the field is negligable. However any charge, no matter how small, will affect the overall electric field and this changes the energy stored in the field.

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  • $\begingroup$ We create a G-field by moving a planet from infinity to the origin. What work is done in this case to create the field? Isn't it 0? Then shouldnt the energy stored in the field be 0? $\endgroup$
    – Sagnik
    Feb 3, 2015 at 8:26
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    $\begingroup$ @Sagy: you create a gravitational field by starting with empty space then increasing the amount of matter present. What you're describing it the interaction of a (non-negligable) mass with an existing field. If you did no work on the planet its velocity and kinetic energy would increase as it fell into the gravitational potential, and it would simply speed past and escape to infinity again. To create a bound system you have to do work on the planet to slow it down enough for it to attain a stable orbit. This work goes into the combined gravitational field of the star and planet. $\endgroup$
    – John Rennie
    Feb 3, 2015 at 9:01
  • $\begingroup$ @John_Rennie but still while the planet would pass the origin the G-potential would fluctuate to some non-zero value and then again to 0, the field though not everlasting, has momentary existence. We are still creating it for a small span of time aren't we? $\endgroup$
    – Sagnik
    Feb 3, 2015 at 9:45

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