# Negative Voltage when Magnet Falls Through Solenoid: Gaining Energy?

• Miraj Kayastha
In summary, when a magnet falls through a solenoid, a voltage is produced, with positive voltage being produced when the magnet enters and negative voltage when it leaves. Voltage is the energy lost by a unit charge traveling from one point to another, and a negative voltage means that a test charge would gain energy by following that path. The sign of the test charge also matters. When a resistor is connected to the solenoid, it will produce heat regardless of the voltage across it, but it is dangerous to talk about potential energy in this scenario due to the non-conservative nature of the electric field in the presence of a changing magnetic field.
Miraj Kayastha
when a magnet is falling through a solenoid, voltage is produced.
Once positive is produced and the when the magnet leaves the solenoid negative voltage is produced.

Voltage is the energy lost by a unit charge when traveling from one point to the other.

So if there is negative voltage produced, does this mean charge gains energy?

Voltage requires a defined path (though because the electric field is a conservative force, the actual path does not matter, only the endpoints). So yes, if you have a negative voltage, then a test charge would gain energy by following that path. Reverse the path and you have a positive voltage which is the energy you have to expend to move the test charge back to the starting position.

EDIT: Should qualify that the sign of your test charge matters too. We are talking about a positive charge above. A negative charge would be the opposite.

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Whatever the sign of the voltage, and whatever the sign of the charge of the test charge, the field will make it move in a way that it gains kinetic energy from the field. It's dangerous to talk about potential energy, because the electric field is not conservative in the presence of a changing magnetic field.
If you hook up a resistor to the solenoid, it will produce heat, both with a negative and a positive voltage across it.

## 1. What does it mean for a magnet to gain energy while falling through a solenoid?

When a magnet falls through a solenoid, it creates a changing magnetic field which induces a negative voltage in the solenoid. This negative voltage results in an electric current flowing through the solenoid, which in turn creates a repulsive force that opposes the motion of the falling magnet. This repulsive force does work on the magnet, effectively transferring energy to it and causing it to gain kinetic energy as it falls.

## 2. How does the negative voltage in a solenoid contribute to the magnet's energy gain?

The negative voltage in the solenoid creates an electric current, which produces a magnetic field that opposes the motion of the falling magnet. This opposition results in a repulsive force on the magnet, which does work on it and transfers energy to it. In other words, the negative voltage in the solenoid indirectly contributes to the magnet's energy gain by creating a repulsive force.

## 3. Is the energy gain of the magnet proportional to the strength of the solenoid's magnetic field?

No, the energy gain of the magnet is not directly proportional to the strength of the solenoid's magnetic field. While a stronger magnetic field may result in a larger negative voltage and electric current, the repulsive force on the magnet is also influenced by other factors such as the mass and velocity of the falling magnet.

## 4. Can a magnet fall through a solenoid without gaining energy?

No, a magnet will always gain energy when falling through a solenoid due to the repulsive force created by the negative voltage and resulting electric current. However, the amount of energy gained may vary depending on factors such as the strength of the magnetic field and the initial conditions of the falling magnet.

## 5. How does this phenomenon relate to energy conservation?

According to the law of conservation of energy, energy cannot be created or destroyed, only transferred or converted from one form to another. In the case of a magnet falling through a solenoid, the energy gained by the magnet is transferred from the magnetic field in the solenoid. This phenomenon demonstrates the principle of energy conservation and conservation of momentum in electromagnetic systems.

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