Magnetic Forces

Forces in Magnetism The existence of magnetic fields is known because of their affects on moving charges. What is magnetic force (F B )? How does it differ from electric force (F E )? What is known about the forces acting on charged bodies in motion through a magnetic field? Magnitude of the force is proportional to the component of the charge’s velocity that is perpendicular to the magnetic field. Direction of the force is perpendicular to the component of the charge’s velocity perpendicular to the magnetic field(B).

Magnetic Force (Lorentz Force) F B = |q|vB sinθ Because the magnetic force is always perpendicular to the component of the charge’s velocity perpendicular to the magnetic field, it cannot change its speed. Force is maximum when the charge is moving perpendicular to the magnetic field ( = 90). The force is zero if the charge’s velocity is in the same direction as the magnetic field ( = 0). Also, if the speed is not changing, KE will be constant as well.

Example #1 A positively charged particle traveling at 7.5 x 10 5 meters per second enters a uniform magnetic field perpendicular to the lines of force. While in the 4.0 x tesla magnetic field, a net force of 9.6 x newton acts on the particle. What is the magnitude of the charge on the particle?

What is the magnetic field (B)? The magnetic field is a force field just like electric and gravitational fields. It is a vector quantity. Hence, it has both magnitude and direction. Units for B: Tesla

Trajectory of a Charged Particle in a Magnetic Field What path will a charge take when it enters a constant magnetic field with a velocity v as shown below? x x x + v  Since the force is always perpendicular to the v and B, the particle will travel in a circle  Hence, the force is a centripetal force.

Earth’s Magnetosphere Magnetic field of Earth’s atmosphere protects us from charged particles streaming from Sun (solar wind)

Aurora Charged particles can enter atmosphere at magnetic poles, causing an aurora

Force on a Current Carrying Wire F B = |q|v x B = qvB sinθ(1) Lets assume that the charge q travels through the wire in time t. F B = (q)vBsinθ When t is factored in, we obtain: F B = (q/t)(vt) Bsinθ (2) Where: q/t = I (current) vt = L (length of wire) Equation (2) therefore reduces to: F B = ILB sinθ

Examples #2 & #3 A wire 0.30 m long carrying a current of 9.0 A is at right angles to a uniform magnetic field. The force on the wire is 0.40 N. What is the strength of the magnetic field? A wire 650 m long is in a 0.46 T magnetic field. A 1.8 N force acts on the wire. What current is in the wire?

Key Ideas Lorentz Force: A charge moving perpendicular to a magnetic field will experience a force. Charged particles moving perpendicular to a magnetic field will travel in a circular orbit. The magnetic force does not change the kinetic energy of a moving charged particle – only direction. The magnetic field (B) is a vector quantity with the unit of Tesla.