Magnetic Force

Moving Charge  A charge in an electric field is subject to a force. Charge at rest or in motion In the direction of field  A charge in a magnetic field is also subject to a force. Only charges in motion Perpendicular to force and velocity  E  B v

Direction of Force  Magnetic force is another kind of vector multiplication. Vector cross product yields a vector  The magnitude is qvB sin .  The direction points according to the right-hand rule.  force points into the page More force = increasing deflection 

Vector Cross Product  The vector cross product applies to any two vectors.  The cross product is perpendicular to the plane holding the two vectors.  The cross product is not commutative. Reversing the order gives an anti-parallel resultReversing the order gives an anti-parallel result

Uniform Field  The magnitude is qvB sin . q = 1.6 x C v = 5.0 x 10 6 m/s B = 3.0 T Angle between v and B is 30° F = 1.2 x N  The direction is based on a positive charge going down. Down cross north is east Force vector points east  An electromagnet produces a 3.0 T uniform magnetic field pointing horizontally north in the gap between its poles.  A proton enters the field heading north at a downward 30° angle with a speed of 5.0 x 10 6 m/s.  Find the magnitude and direction of the force.

Particle Tracks  Particles like electrons and protons turn in a magnetic field.  Tracks are captured on film.  Curvature is related to the velocity. Fermilab photo from the 15’ bubble chamber

Circular Path  A charge that moves perpendicular to a uniform field stays perpendicular to the field. Uniform circular motion  The magnetic force is a centripetal force. Field into page

Cyclotron  The size of the circle assumes uniform circular motion. r = mv/qB q = 1.6 x C v = 5.0 x 10 6 m/s B = 3.0 T m = 1.6 x kg r = 1.7 x m  The proton in the earlier example moves in a circular path.  Find the radius of the circle. next