Hello again,

I just checked to be sure and yes the following formula is the force on a (straight not curved) current carrying wire within a magnetic field , B.

where I is the current flowing through the wire.

B is the magnetic field the wire is within.

L is a vector, whose magnitude is the length of wire (measured in meters), and whose direction is along the wire, aligned with the direction of

conventional current flow.

Although an alternative formula is equivalent, and that is:

Where the vector direction is now associated with the current variable, instead of the length variable. The two forms are equivalent.

If a curved wire is immersed in a B field, the force acting upon it can be found by integrating each

infinitesimal segment of wire

*d***ℓ**, then adding up all these forces through integration, which yields:

This is for a curved wire in a B field. If the wire is straight then the integral just comes out to be I times the total length, L crossed with the B field.

So this is the formula I believe you were referring to, except that you were summing the B field with the product of the current and the length and not crossing that product with the B field.

These equations are known as the Lorentz force and they yield the force on a wire itself due to the charges flowing in the wire being displaced by the B field which acts to push them to one surface of the wire which creates a real force on the wire trying to push it out in the direction the charges are pushing against the surface of the wire they are traveling through.

It can be derived from the Lorentz force law and the definition of electrical current. So you do not want to use this function as you want to know the displacement force due to both an E field and a B field that charges are passing through with some velocity, v. So you want to use:

where q is the charge, both in value and in sign, of the ions or electrons that are passing through these fields.

E is the electric field in volts per meter

v is the velocity vector of the charge that is moving through these fields in meters per second.

B is the magnetic field in Tesla's or Webber's per squared meter.

I believe this is all you need to answer your own question now.

Many smiles,

Craig