# Acceleration due to gravity on Coil vs Insulator

Consider I have a coil with a length of $5m$ and made up of copper wire with a diameter of cross-section $d$ and wrapped around an imaginary axis with radius $R$ with mass $M$.

Now consider an insulator made up of a glass of mass $M$ of $5m$ of diameter $D$.

If both were taken very high in the atmosphere but not away from the gravity of the earth. Then it is dropped from that point at the same level without providing any external force.

My question is that which object will move faster

• Conductor. OR
• Insulator.

I have been taught that every object of any mass will have same acceleration due to gravity but electromagnetism course taught us that a coil will produce induction and it will slow down or speed up the coil.

Which theory is true?

The answer always lies in the equation of motion.

For the insulator, the force equation is:

$$\vec{F} = m\vec{g}$$

$$\vec{a} = \vec{g}$$

Any object which is falling down only due to gravity experiences the same acceleration.

In case of an inductor, there is more than one force acting. For the inductor (coil), the force equation is:

$$\vec{F} = m\vec{g} - F_\phi$$ $$\vec{a} = \vec{g} -\frac{F_\phi}{m}$$

where $F_\phi$ is the force due to changing magnetic flux. The earth's magnetic field is not constant; it varies as the position changes. Moreover, as the coil falls, it could change direction. These two factors can cause a change in magnetic flux which induces eddy currents in the coil. These eddy currents oppose the motion of the inductor through the magnetic field. Therefore, the inductor accelerates slower than the insulator. Speaking honestly, the effect of earth's magnetic field is negligible.

Both the theories are correct.