Chapter 19: Magnetic Forces and Fields. Magnetic Fields Magnetic Force on a Point Charge Motion of a Charged Particle in a Magnetic Field Crossed E and B fields Magnetic Forces on Current Carrying Wires Torque on a Current Loop Magnetic Field Due to a Current Amp è re’s Law
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
All magnets have at least one north pole and one south pole.
Field lines emerge from north poles and enter through south poles.
Opposite magnetic poles attract and like magnetic poles repel.
If a magnet is broken in half you just end up with two magnets.
Note the orientation of the magnetic poles!
Evidence for magnetic pole reversals has been found on the ocean floor. The iron bearing minerals in the rock contain a record of the Earth’s magnetic field.
The magnetic force on a point charge is:
The unit of magnetic field (B) is the tesla (1T = 1 N/Am).
The magnitude of FB is:
where vsin is the component of the velocity perpendicular to the direction of the magnetic field. represents the angle between v and B.
Draw the vectors tail-to-tail to determine .
For a general cross product:
The right-hand rule is: using your right hand, point your fingers in the direction of A and curl them in the direction of B. Your thumb points in the direction of C.
Example (text problem 19.15): An electron moves with speed 2.0105 m/s in a 1.2 Tesla uniform magnetic field. At one instant, the electron is moving due west and experiences an upward magnetic force of 3.210-14 N. What is the direction of the magnetic field?
The angle can be either north of west OR north of east.
A positively charged particle has a velocity v (orange arrow) as shown. The magnetic field is into the page.
The magnetic force, at this instant, is shown in blue. In this region of space this positive charge will move CCW in a circular path.
A charged particle is shot into a region of known magnetic field.
Particles of different mass will travel different distances before striking the detector. (v, B, and q can be controlled.)
Cyclotrons are used in the production of radioactive nuclei. For medical uses see the website of the Nuclear Energy Institute.
Synchrotrons are being tested for use in treating tumors.
If a charged particle has a component of its velocity perpendicular to B, then its path will be a circle. If it also a component of v parallel to B, then it will move forward as well. This resulting path is a helix.
If a charged particle enters a region of space with both electric and magnetic fields present, the force on the particle will be
Consider a region of space with crossed electric and magnetic fields.
Charge q>0 with velocity v
The net force equal zero will occur when v=E/B.
This region of space (with crossed E and B fields) is called a “velocity selector”. It can be used as part of a mass spectrometer.
The force on a current carrying wire in an external magnetic field is
L is a vector that points in the direction of the current flow. Its magnitude is the length of the wire.
and its direction is given by the right-hand rule.
Example (text problem 19.43): A 20.0 cm by 30.0 cm loop of wire carries 1.0 A of current clockwise.
(a) Find the magnetic force on each side of the loop if the magnetic field is 2.5 T to the left.
Left: F out of page
Top: no force
Right: F into page
Bottom: no force
The magnitudes of the nonzero forces are:
(b) What is the net force on the loop?
N = number of turns of wire in the loop.
I = the current carried by the loop.
A = area of the loop.
B = the magnetic field strength.
= the angle between A and B.
Because there is a torque on the current loop, it must have both a north and south pole. A current loop is a magnetic dipole. (Your thumb, using the above RHR, points from south to north.)
Moving charges (a current) create magnetic fields.
where 0 = 410-7 Tm/A is the permeability of free space.
The direction of the B-field lines is given by a right-hand rule. Point the thumb of your right hand in the direction of the current flow while wrapping your hand around the wire; your fingers will curl in the direction of the magnetic field lines.
The B-field lines of this wire are CCW.
Note: The field (B) is tangent to the field lines.
Example (text problem 19.62): Two parallel wires in a horizontal plane carry currents I1 and I2 to the right. The wires each have a length L and are separated by a
(a) What are the magnitude and direction of the B-field of wire 1 at the location of wire 2?
Into the page
(b) What are the magnitude and direction of the magnetic force on wire 2 due to wire 1?
F12 toward top of page (toward wire 1)
(c) What are the magnitude and direction of the B-field of wire 2 at the location of wire 1?
Out of the page
(d) What are the magnitude and direction of the magnetic force on wire 1 due to wire 2?
F21 toward bottom of page (toward wire 2)
(e) Do parallel currents attract or repel? They attract.
(f) Do antiparallel currents attract or repel? They repel.
The strength of the B-field at the center of the (single) wire loop is:
A solenoid is a coil of wire that is wrapped in a cylindrical shape.
The field inside a solenoid is nearly uniform (if you stay away from the ends) and has a strength:
Where n=N/L is the number of turns of wire (N) per unit length (L) and I is the current in the wire.
Ampère’s Law relates the magnetic field on a path to the net current cutting through the path.
(a) What is the net current though the interior of loop 1?
Assume currents into the page are negative and current out of the page are positive.
Loop 1 encloses currents -3I, +14I, and -6I. The net current is +5I or 5I out of the page.
(b) What is the net current though the interior of loop 2?
Loop 2 encloses currents -16I and +14I. The net current is -2I or 2I into the page.
Here the B-field is tangent to the path everywhere (hence the choice of a circular path). The circulation is
where I is the net current that cuts through the circular path.
If the wire from the previous page carries a current I then the magnetic field at distance r from the wire is
Ferromagnetic materials have domains, regions in which its atomic dipoles are aligned, giving the region a strong dipole moment.
When the domains are aligned, the material will have a net magnetization.