# Conservation of Energy on Current-Carrying Wire in Magnetic Field

• yosimba2000
In summary, the force on a current-carrying wire is equal to the product of the current, length of the wire, and the magnetic field strength. When the magnetic field is doubled, the force on the wire also doubles, resulting in a longer distance traveled and more work done on the wire. However, the electrical energy input remains the same. This can be explained by using differential equations to describe the system.
yosimba2000
So force on a current carrying wire = ILxB.

If I have a bunch of bar magnets making a uniform magnetic field of strength B, then a 1 meter long wire of 0 ohms carrying 1 Amp, the force on that wire is (1)(1)xB = 1B. If I let that force move the wire for a time T, let's assume the wire moved a distance X. So the work done on the wire is 1BX joules.

Now let's say I keep everything the same but double the magnetic field using stronger magnets. So now Force on this wire is (1)(1)(2B) = 2B. Since the force is double the original and acting on the same object, if I let it act upon the wire for the same amount of time T, the wire will move a longer distance than the original X, let's say 1.5X. So the work done on this wire is (2B)(1.5X) = 3BX joules.

My electrical energy input was the same in both scenarios: E = IVT. I, V, and T were the same in both experiments, but the energy exerted on the wires were different by a factor of 3. How? I understand the force is larger, but how did I get 1BX and 3BX joules of energy for the same electrical input? It must have come from somewhere, but where? It's not as though the magnets "lost" magnetic energy and became less magnetic.

I suggest you can try to describe your system with differential equations.

yosimba2000 said:
I, V, and T were the same in both experiments
Are you sure about that?

nasu

## 1. What is conservation of energy?

The law of conservation of energy states that energy cannot be created or destroyed, but can only be converted from one form to another. This means that the total amount of energy in a closed system remains constant over time.

## 2. How does conservation of energy apply to a current-carrying wire in a magnetic field?

When a current-carrying wire is placed in a magnetic field, the magnetic force exerted on the wire causes it to experience a change in motion. This change in motion requires a transfer of energy, which is provided by the electric potential energy of the current. However, according to the law of conservation of energy, this energy cannot be created or destroyed, so it is converted into other forms, such as kinetic energy and heat.

## 3. What is the relationship between the current, magnetic field, and energy conservation in this system?

The amount of energy transferred in a current-carrying wire in a magnetic field depends on the strength of the magnetic field, the amount of current flowing through the wire, and the length of the wire. The more current and the stronger the magnetic field, the greater the amount of energy transferred. However, the total amount of energy remains constant, as dictated by the law of conservation of energy.

## 4. Can conservation of energy be violated in this system?

No, the law of conservation of energy is a fundamental principle of physics and cannot be violated. In a closed system, the total amount of energy remains constant, so any changes in energy must be accounted for through conversion to other forms of energy.

## 5. How is the concept of conservation of energy applied in real-world situations involving current-carrying wires in magnetic fields?

Conservation of energy is a crucial concept in designing and understanding the operation of devices such as electric motors and generators, which rely on the interaction between current-carrying wires and magnetic fields to convert electrical energy into mechanical energy and vice versa. By applying the principles of conservation of energy, engineers can optimize the efficiency and performance of these devices.

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