Physics · Ch 3 — Magnetism and Magnetic Effects of Electric Current
Force on a Moving Charge in a Magnetic Field
Force on a Moving Charge in a Magnetic Field
When a charge moves with velocity in a field , it feels the magnetic force
where is the angle between and . This says: (1) ; (2) ; (3) ; (4) ; (5) is always perpendicular to both and (being their cross product); (6) reversing the sign of reverses the direction of for otherwise identical motion; and (7) if is parallel to (), -- a charge moving exactly along the field lines feels no magnetic force at all. This last property defines the SI unit of field: the field is one tesla if a unit charge moving with uni …
What this figure shows. Two panels compare a positive charge and a negative charge, both moving with the same velocity v through the same field B. For the positive charge, the resulting force Fm is drawn in one direction (obtained from v cross B); for the negative charge, moving identically in the same field, the force Fm is drawn in exactly the opposite direction, showing that reversing the sign of the charge reverses the force even though not …
Worked out. A charge q moves with velocity v along +y in field B, examined in three cases. (a) B along +y (parallel to v): Fm = q(v j-hat x B j-hat) = 0, since a vector crossed with itself is zero -- no force acts when velocity and field are parallel. (b) B along +z: Fm = q(v j-hat x B k-hat) = qvB i-hat, a force of magnitude qvB along +x. (c) B in the y-z plane at angle theta to v, B = B cos(theta) j-hat + B sin(theta) k-hat: Fm = q(v j-hat) x B = qvB sin(theta) i-hat, a force of magnitude qvB sin(theta) along +x. In every case the force comes out perpendicular to both v and …