# B How is energy stored in these fields?

1. Sep 16, 2018

### AchillesWrathfulLove

How is energy stored in the following fields, please give an example for each field:

1. Electric field
2. Magnetic field
3. Gravitational field

2. Sep 16, 2018

### Delta2

1. Consider a capacitor of capacitance C. The energy required to charge the capacitor to charge $Q_0$ is the energy that will be stored in the e-field between its plates. Why it is required energy to charge from charge 0 to charge $Q_0$? Consider a capacitor that is already charged at charge $q$ and we want to charge it to charge $q+dq$. Therefore we have to do work against the E-field that exists between its plates to transfer charge +dq from the negative plate to the positive plate and this work is $dW=Vdq=\frac{q}{C}dq$ . So the total work done to charge it from 0 to charge $Q_0$ is $W=\int dW=\int_0^{Q_0}\frac{q}{C}dq=\frac{1}{2}\frac{Q_0^2}{C}$ and this work is stored as E-field energy in the E-field between its plates.
2. Consider an inductor of inductance L. The energy required to "charge" the inductor to current $I_0$ is the energy that will be stored in the magnetic field inside the turns of the coil. Energy is required because we know that an inductor "resists" a change to its current from $I$ to $I+dI$ (due to Lenz's law). The work required to change the current from $I$ to $I+dI$ is $dW=VIdt=L\frac{dI}{dt}Idt=LIdI$ so the total work required is $W=\int dW=\int_0^{I_0}LIdI=\frac{1}{2}LI_0^2$.

3. Sep 16, 2018

### Staff: Mentor

Please post homework and homework type questions in the homework sections, and use the template.