Magnitude of the Magnetic Force

Magnitude of the Magnetic Force

How does one magnet attracts another? The answer relies on the fact that all magnetism relies on current, the flow of charge. Magnetic fields exert forces on moving charges, and so they exert forces on other magnets, all of which have moving charges.

The magnetic force on a moving charge is one of the most fundamental known. The magnetic force is as important as the electrostatic or Coulomb force. Yet the magnetic force is more complex, in both the number of factors that affects it and in its direction, than the relatively simple Coulomb force. The magnitude of the magnetic force $F$ on a charge $q$ moving at a speed $v$ in a magnetic field of strength $B$ is given by:

$F=qvBsin(\theta )$

where θ is the angle between the directions of $v$ and $B$. This formula is used to define the magnetic strength $B$ in terms of the force on a charged particle moving in a magnetic field. The SI unit for magnitude of the magnetic field strength is called the tesla (T) in honor of the brilliant and eccentric inventor Nikola Tesla (1856–1943), who made great contributions to our understanding of magnetic fields and their practical applications. To determine how the tesla relates to other SI units, we solve $F=qvBsin(\theta )$ for $B$:

$B = \frac{F}{qvsin(\theta )}$

Because sinθ is unitless, the tesla is

$1T = \frac{1N}{C*m/s} = \frac{1N}{A*m}$

Another smaller unit, called the gauss (G), where 1 G=10⁻⁴ T, is sometimes used. The strongest permanent magnets have fields near 2 T; superconducting electromagnets may attain 10 T or more. The Earth's magnetic field on its surface is only about 5×10⁻⁵ T, or 0.5 G.

The direction of the magnetic force $F$is perpendicular to the plane formed by $v$ and $B$ as determined by the right hand rule, which is illustrated in Figure 1 . It states that, to determine the direction of the magnetic force on a positive moving charge, you point the thumb of the right hand in the direction of $v$, the fingers in the direction of $B$, and a perpendicular to the palm points in the direction of $F$. One way to remember this is that there is one velocity, and so the thumb represents it. There are many field lines, and so the fingers represent them. The force is in the direction you would push with your palm. The force on a negative charge is in exactly the opposite direction to that on a positive charge.

Right Hand Rule

Magnetic fields exert forces on moving charges. This force is one of the most basic known. The direction of the magnetic force on a moving charge is perpendicular to the plane formed by v and B and follows right hand rule–1 (RHR-1) as shown. The magnitude of the force is proportional to q, v, B, and the sine of the angle between v and B.