# 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.