Physics equations/Magnetic forces

Magnetic forces: Lorentz and Laplace]

https://en.wikipedia.org/w/index.php?title=Magnetic_field&oldid=582423833 The Lorentz force is the combination of electric and magnetic force on a point charge due to electromagnetic fields. If a particle of charge q moves with velocity v in the presence of an electric field E and a magnetic field B, then it will experience a force

${\vec {F}}=q\left({\vec {E}}+{\vec {v}}\times {\vec {B}}\right)$

(in SI units). Variations on this basic formula describe the magnetic force on a current-carrying wire (sometimes called Laplace force), the electromotive force in a wire loop moving through a magnetic field (an aspect of Faraday's law of induction), and the force on a particle which might be traveling near the speed of light (relativistic form of the Lorentz force).

If the charged particles are travelling in a wire we have the Laplace force:

${\vec {F}}=I\int d{\vec {\ell }}\times {\vec {B}}$

• Problem: A wire segment that is 2.5 meters long carries a current of 12 amps in a 3.5 Tesla field. What is the force on the segment if the angle between the wire and the magnetic field is 30 degrees? *

(click for answer)

Since sin 30° = ½, we have

$\mathbf {F} =\left|I\int d{\boldsymbol {\ell }}\times \mathbf {B} \right|=(12)(2.5)(3.5)(0.5)=52.5{\text{N}}.$

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If $x\neq 0$, then

$B={\frac {\mu _{0}I}{2}}{\frac {a^{2}}{(x^{2}+a^{2})^{3/2}}}$.

Here only the first (and far simpler) problem is solved. Both variants of the right-hand rule stipulate that each element of length in the line integral contributes an element of magnetic field that points in the same direction, as shown in the figures below: