Peoples Physics Concepts

http://www.ck12.org Chapter 14. Magnetism

14.3 Current and Magnetism

• Analyze and solve problems involving current carrying wires in magnetic fields.

Students will learn to analyze and solve problems involving current carrying wires in magnetic fields.

Key Equations

Fwire=LIBsin(θ) Force on a Current Carrying Wire

In this equation,Lrefers to the length of the wire,Ito the electric current,Bthe magnitude of the magnetic field

andθis the angle between the direction of the current and the direction of the magnetic field.

Bwire=

μ 0 I

2 πr

Magnetic field at a distancerfrom a current-carrying wire

Whereμ 0 = 4 π× 10 −^7 Tm/A Permeability of Vacuum (approximately same for air also)

Force on a Wire

Since a wire is nothing but a collection of moving charges, the force it will experience in a magnetic field will
simply be the vector sum of the forces on the individual charges. If the wire is straight — that is, all the charges are
moving in the same direction — these forces will all point in the same direction, and so will their sum. Then, the
direction of the force can be found using the second right hand rule, while its magnitude will depend on the length
of the wire (denotedL), the strength of the current, the strength of the field, and the angle between their directions:
Two current-carrying wires next to each other each generate magnetic fields and therefore exert forces on each
other: