# Magnetic Force on a Current-Carrying Wire Calculator

Created by Kenneth Alambra
Last updated: Sep 16, 2022

In this Magnetic Force on a Current-Carrying Wire Calculator, you will learn how to calculate the magnetic force on a wire with an electric current flowing through it and how to use this tool.

Moving a magnetic field close to a moving electric charge produces what is called the Lorentz force. That is the magnetic force we are looking for in this calculator. Keep on reading to start learning! You can also check the helical coil calculator, where we described the electrical and magnetic properties of a solenoid.

## How to calculate the magnetic force on a wire

We only need a few parameters to calculate the magnetic force on a wire. All of which is directly proportional to the magnetic force on a wire. That means we only have to multiply each of them together, as shown in this equation:

$F = B\times I\times L\times \sin(\alpha)$

Where:

• $F$ is the magnetic force strength in newtons (N);
• $B$ is the magnetic field strength in tesla (T);
• $I$ is the amperage of the electric current flowing through the wire in amperes (A);
• $L$ is the length of the wire in meters (m);
• $\alpha$ is the angle in radians (rad) between the electric current's direction and the magnetic field lines' direction.

We usually assign $\small\alpha$ to be equal to $\small\tfrac{\pi}{2}\ \text{radians}$ (or $\small90^\circ$) to find the maximum electromagnetic force around any magnetic object; and also because the magnetic field is always perpendicular to the electric current's direction. Since $\sin(\tfrac{\pi}{2}) = 1$, that means to find the maximum magnetic force around a wire, we can use this equation:

$F = B\times I\times L$

On the other hand, by considering $\small\alpha=0\ \text{rad}$, we won't get any magnetic force on our wire since $\small\sin(0) = 0$. That is because magnetic fields don't interact with electric current and charges that have the same direction as them.

🔎 But what happens if we move two magnetic fields close to each other? Learn about the interaction between two magnetic fields by checking out our magnetic force between current-carrying wires calculator.

## How to use this magnetic force on a current-carrying wire calculator

Remembering the magnetic force on a wire calculation formula is very easy. But using our Magnetic Force on Current-Carrying Wire Calculator is much easier! All you have to do is:

1. Enter the magnetic field strength where you'll place your straight piece of wire. Say $0.5\ \text{tesla}$.
2. Input the amperage of the electric current passing through your wire. Let's say about $2\ \text{amperes}$.
3. Type in the length of your straight wire. Let's say it's $20\ \text{cm}$. For that, you must first change the length's unit to $\text{centimeters (cm)}$, then type $20$ for the length.

After that, our Magnetic Force on a Current-Carrying Wire Calculator will display the magnetic force in newtons by default. For our example, we should obtain $0.2\ \text{N}$.

Again, that is for the maximum magnetic force strength around your wire at $\alpha = 90^\circ$. You can click on the Advanced mode button below our tool to access the angle variable if you want to change its value.

If you find this interesting, perhaps you would also like our Magnetic Field of Straight Current-Carrying Wire. There you'll learn the basics of how an electromagnet works.

Kenneth Alambra
Magnetic field
T
Current
A
Length
ft
Force
N
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