Certain iron containing materials hae been known to attract or repel each other. Compasses align to the magnetic field of earth. Analogous to positie and negatie charges, eery magnet has a north and a south pole (but always as a pair). Magnetic fields can be created by electrical currents.
+q q, // 0 0, opposite q 0, direction q 0, sin
q q sin Magnetic ield, : Tesla (T)=N/(C.m/s)=N/(A.m) Right Hand Rule Magnetic ield Representation
q qe E Electric forces act in the direction of the electric field, magnetic forces are perpendicular to the magnetic field. A magnetic force exists only for charges in motion. The magnetic force of a steady magnetic field does no work when displacing a charged particle. The magnetic field can alter the direction of a moing charged particle but not its speed or its kinetic energy.
Consider a positie charge moing perpendicular to a magnetic field with an initial elocity,. The force is always at right angles to and its magnitude is, q So, as q moes, it will rotate about a circle and and will always be perpendicular. The magnitude of will always be the same, only its direction will change.
To find the radius and frequency of the rotation: The radial force mar 2 q m r r m q The angular speed The period T r q m 2r 2 2m q Cyclotron frequency
Electron beam in a magnetic field V r V = 350 V r = 7.5 cm q = e = 1.6 x 10-19 C m = m e = 9.11 x 10-31 kg K 1 2 U m e 2 ev =? =? 2 7 ev m e 1.1110 m / s r m q m er 8.410 e 4 T q m e m e 1.510 8 rad / s
Helical Motion Cosmic Rays in the Complex ields x, y and z Van Allen elt Magnetic ottles
Essentially it is the total electric and magnetic force acting upon a charge. qe q Velocity Selector Mass Spectrometer e E m 0 q r E
Magnetic force acts upon charges moing in a conductor. The total force on the current is the integral sum of the force on each charge in the current. In turn, the charges transfer the force on to the wire when they collide with the atoms of the wire.
d q q, nal q d qna I d L I or a straight wire in a uniform field s Id d b a d I s or an arbitrary wire in an arbitrary field
b a d I s s b a d I L I The net magnetic force acting on a cured wire in a uniform magnetic field is the same as that of a straight wire between the same end points.
I s d d s 0 0 Net magnetic force acting on any closed current loop in a uniform magnetic field is zero.
On the cured wire d2 I ds s R ds Rd d IRsind Isinds On the straight wire IL 2IR 1 Directed out of the board 2 2 IRsind IR sind 0 2 2IR 0 Directed in to the board 1 2 0
If the field is parallel to the plane of the loop or 1 and 3, L 0 0 or 2 and 4, 4 Ia 2 b b b Ia Ia max max 2 2 Iab 4 2 2 b 2 max IA
If the field makes an angle with a line perpendicular to the plane of the loop: a a 2 sin 4 sin 2 2 b b Ia sin Ia sin 2 2 IAsin Iabsin τ IA
A rectangular loop is placed in a uniform magnetic field with the plane of the loop perpendicular to the direction of the field. If a current is made to flow through the loop in the sense shown by the arrows, the field exerts on the loop: 1. a net force. 2. a net torque. 3. a net force and a net torque. 4. neither a net force nor a net torque.
μ τ IA μ (Amperes.m 2 ) If the wire makes N loops around A, τ Nμ loop μ coil The potential μ energy of the loop is: U
q E H d V d V H H d qe d I nqa I nqt H d RH I t
The right hand rule Magnetic forces on charged particles Charged particle motion Magnetic forces on current carrying wires Torque on loops and magnetic dipole moments
Reading Assignment Chapter 30 Sources of the Magnetic ield WebAssign: Assignment 7