Right-Hand Rules:  A Guide to finding the Direction of the Magnetic
Force

Fmagnetic
- The force a magnetic field exerts on a moving charge

When a charge is placed in a magnetic field, that charge
experiences a magnetic force; when two conditions exist:
1)  the
charge is moving relative to the magnetic field,
2)  the charge's
velocity has a component perpendicular to the direction of the magnetic
field

The Right-Hand Rules apply to positive charges or
positive (conventional) current

When using the Right-Hand Rules, it is important to remember
that the rules assume charges move in a conventional current (the
hypthetical flow of positive charges).  In order to apply either
Right-Hand Rule to a moving negative charge, the velocity (v) of that
charge must be reversed--to represent the analogous conventional
current.

Making illustrations of magnetic field and charge
interactions in 3D

Because the force exerted on a moving charge by a magnetic
field is perpendicular to both the the velocity of the charge and the
direction of the field, making illustrations of these interactions
involves using the two symbols on the left to denote movement into or out
of the plane of the page.

Right-Hand Rule #1 (RHR #1)

Right-Hand Rule #1 determines the
directions of magnetic force, conventional current and the magnetic field.
Given any two of theses, the third can be found.

Using your right-hand:
point your index finger in the
direction of the charge's velocity, v, (recall conventional
current).

Point your middle finger in the direction of the magnetic field, B.

Your thumb now points in the direction of the magnetic force,
Fmagnetic.

Right-Hand Rule #2 (RHR #2)

Right-Hand Rule #2 determines the direction of the magnetic
field around a current-carrying wire and vice-versa

Using your right-hand:
Curl your fingers into a
half-circle around the wire, they point in the direction of the magnetic
field, B

Point your thumb in the direction of the conventional current.

Applying the Right-Hand Rules:

The Right-Hand Rules give only the direction of the magnetic field.  In
order to determine the strength of a magnetic field , some useful mathematical
equations can be applied.

For a long, straight wire, the magnetic field, B is:

B = moI / 2pr;where,
mo
=  4p x 10-7 T · m
/ A and os called the permeability of free space, r is the radial distance
from the wire in meters, and I is the current in amperes.

For a single loop of  wire, the magnetic field, B
through the center of the loop is:

B = moI / 2R;where,
mo is the
permeability of free space, and R is the radius of the the circular loop
of wire, measured in meters.  Both the fields for a coil of wire and
a solenoid can be constructed from this
equation.

Questions to Consider:
1.  A proton is travelling with a speed of
5.0 x 106m / s, when it encounters a magnetic
field of magnitude 0.40 T and that is perpendicular to the velocity of the
proton.  Make a sketch of this situation and indicating the directions of
the velocity of the proton, the magnetic field and the magnetic force.

2.  Here, a long,
straight wire carries a current, I,  of 3.0 A.  A particle, q
with a charge of +6.5 x 10-6 C, moves parallel to the wire in the direction
shown, at a distance of r = 0.050 m and a speed of v = 280 m /
s.  Determine the magnitude and direction of the magnetic field
experienced by the charge.

References:
Cutnell, J.and Johnson, K. (1998), Physics, Vol. 2,
Wiley: NY, p. 631, 33, 46, and 49.

This page contributed to by Camilo Tafur and Dan MacIssac

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