The Q–ℰ–ℬ triangle, a schematic reminder of the fundamental laws connecting the concepts of charge, electric field, and magnetic field.
Each of the three electromagnetic quantities is capable of influencing the other two. Associated with each of the six arrows in the figure is one fundamental law of electromagnetism. The arrow from Q to ℬ designates the influence of charge on magnetic field, the arrow from ℰ to Q designates the influence of electric field on charge, and so on.
(1) Q→ℰ
In words: Charge creates electric field.
In symbols:
Direction: Electric field is directed radially away from positive charge and toward negative charge.
(2) ℰ→Q’
In words: An electric field exerts a force on a charge.
In symbols:
F = Q’ℰ .
Direction: The electric force on a positive charge is parallel to the acting electric field. On a negative charge, the force is opposite to the direction of the field.
(3) Q→ℬ
In words: Moving charge creates magnetic field.
In symbols:
v⟂ is the component of the particle’s velocity perpendicular to a line drawn from the location of the moving charge to the point of observation.
Direction: Let the right thumb point in the direction of motion of the charge and the fingers of the right hand point along the line from the charge to the point of observation. Then the direction in which the right palm pushes is the direction of the magnetic field created at the point of observation if the moving charge is positive. If the charge is negative, use the same rule, but with the left hand instead of the right (or use the right hand and reverse the conclusion).
(4) ℬ→Q’
In words: A magnetic field exerts a force on a moving charge.
In symbols:
v⟂ is the component of the particle’s velocity perpendicular to the direction of the magnetic field.
Direction: Let the right thumb point in the direction of motion of the charge and the fingers of the right hand point in the direction of the magnetic field. Then the direction in which the right palm pushes is the direction of the force if the moving charge is positive. If the charge is negative, use the same rule, but with the left hand instead of the right (or use the right hand and reverse the conclusion).
(5) ℬ→ℰ
In words: A changing magnetic field creates an electric field.
(6) ℰ→ℬ
In words: A changing electric field creates a magnetic field.
I do not present mathematical expressions for these last two laws, but remark that here as in all other ways in which electricity and magnetism interact, perpendicularity is the rule. The direction of the induced field is perpendicular to the direction of change of the inducing field.