If the force increases when the current increase what can you say about the force on a current element as a function of the current?
I would say the force is proportional to the current
To determine the relationship between the force on a current element and the current, we can consider Ampere's law and the Biot-Savart law.
Ampere's law states that the line integral of the magnetic field around a closed loop is equal to the product of the current flowing through the loop and the permeability of the medium:
∮B⋅dl = μ₀I
Where:
- B is the magnetic field
- dl is an infinitesimal element of the closed loop
- μ₀ is the permeability of free space
- I is the current flowing through the closed loop
The Biot-Savart law calculates the magnetic field due to a small current element:
d𝐵 = (𝜇₀ / 4𝜋) * [(𝐼 * d𝐥) × 𝐫̂] / r²
Where:
- d𝐵 is the magnetic field due to the current element
- 𝜇₀ is the permeability of free space
- 𝐼 is the current passing through the current element
- d𝐥 is an infinitesimal element of the current element
- 𝐫̂ is the direction vector from the current element to the point
- r is the distance from the current element to the point
Based on these two laws, let's consider a scenario where the current passing through a closed loop increases. According to Ampere's law, the line integral of the magnetic field around the loop will also increase. This means that the magnetic field at every point on the loop will increase.
Now, using the Biot-Savart law, we can say that since the current has increased, the magnitude of the magnetic field due to each current element also increases. The direction of the magnetic field depends on the direction of the current element and the distance from the current element to the point of interest.
Therefore, as the current increases, the force on a current element is expected to increase as well. This occurs because the magnetic field produced by each current element becomes stronger, resulting in a larger force on neighboring current elements.
In summary, when the current increases, the force on a current element is expected to increase as well. This conclusion is supported by Ampere's law and the Biot-Savart law, which describe the relationship between the current, magnetic field, and force in electromagnetic systems.