WEEK 4 Day 1 Magnetic field Biot-Savart

Magnetic Fields Produced by Currents Example: A Current Exerts a Magnetic Force on a Moving Charge The long straight wire carries a current of 3.0 A. A particle has a charge of +6.5x10-6 C and is moving parallel to the wire at a distance of 0.050 m. The speed of the particle is 280 m/s. Determine the magnitude and direction of the magnetic force on the particle.

Magnetic Fields Produced by Currents

Magnetic Fields Produced by Currents Current carrying wires can exert forces on each other.

The Magnetic Force Between Two Parallel Conductors Consider two long, straight, parallel wires, separated by a distance a and each carrying a steady current We can find the force on one wire due to the magnetic field set up by the other wire

22.8 The Magnetic Force Between Two Parallel Conductors The force is Rewriting in terms of the force per unit length: The equation applies to both wires

The Magnetic Force Between Two Parallel Conductors When the currents are in opposite directions, the magnetic forces are reversed and the wires repel each other Parallel conductors carrying currents in the same direction attract each other Parallel conductors carrying currents in opposite directions repel each other

Suspending a Wire Two infinitely long, parallel wires are lying on the ground a distance a = 1.00 cm apart. A third wire, of length L = 10.0 m and mass 400 g, carries a current of I1 = 100 A and is levitated above the first two wires, at a horizontal position midway between them. The infinitely long wires carry equal currents I2 in the same direction, but in the direction opposite that in the levitated wire. What current must the infinitely long wires carry so that the three wires form an equilateral triangle?

Suspending a Wire .

Suspending a Wire Find the total magnetic force in the upward direction on the levitated wire: Find the gravitational force on the levitated wire:

Suspending a Wire Substitute numerical values:

Suspending a Wire Apply the particle in equilibrium model by adding the forces and setting the net force equal to zero: Solve for the current in the wires on the ground:

Magnetic Field of a Current Loop A circular ring of radius a carries a current I as shown. Calculate the magnetic field at a point P along the axis of the ring at a distance x from its center. Draw a figure. Write down the starting equation. It tells you what to do next. Draw a figure. y I a x x P z

Magnetic Field of a Current Loop A circular ring of radius a carries a current I as shown. Calculate the magnetic field at a point P along the axis of the ring at a distance x from its center. y dl dB I  dBy 90- a dl is in the yz plane. r is in the xy plane and is perpendicular to dl.* Thus 90-  x x P dBx z Also, dB must lie in the xy plane* (perpendicular to dl) and is perpendicular to r. *Only when dl is centered on the y-axis!

y dl dB I  dBy 90- a 90-  x x P dBx z By symmetry, By will be 0.

y I dl dBy dBz x x P dBx z When dl is not centered at z=0, there will be a z-component to the magnetic field, but by symmetry Bz will be zero.

I, x, and a are constant as you integrate around the ring! dl dB I  dBy 90- a 90-  x x P dBx z I, x, and a are constant as you integrate around the ring!

At the center of the ring, x=0. y At the center of the ring, x=0. dl dB I  dBy 90- a 90-  x x P dBx z For N tightly packed concentric rings (a tight coil)…

Magnetic Fields Produced by Currents A LOOP OF WIRE center of circular loop

Magnetic Fields Produced by Currents Finding the Net Magnetic Field A long straight wire carries a current of 8.0 A and a circular loop of wire carries a current of 2.0 A and has a radius of 0.030 m. Find the magnitude and direction of the magnetic field at the center of the loop.

Magnetic Fields Produced by Currents

Magnetic Fields Produced by Currents The field lines around the bar magnet resemble those around the loop.

Magnetic Fields Produced by Currents

Magnetic Fields Produced by Currents A SOLENOID number of turns per unit length Interior of a solenoid

Magnetic Fields Produced by Currents A cathode ray tube.

properties of materials. Magnetic Materials The intrinsic “spin” and orbital motion of electrons gives rise to the magnetic properties of materials. In ferromagnetic materials groups of neighboring atoms, forming magnetic domains, the spins of electrons are naturally aligned with each other.

Magnetic Materials