Ph126 Spring 2008Lecture #8

Magnetic Fields Produced by

Moving Charges  Prof. Gregory Tarlégtarle@umich.edu

Last Lecture: Magnetic Forces Moving charges can

experience forces in magnetic fields: Magnitude:

Direction: Right-Hand Rule

Magnetic force does no work on the moving charge

Measure magnetic field in Tesla (T)

sinvBqF

Electric vs. Magnetic Forces The electric force is always in the direction of the

electric field, but the magnetic force is always perpendicular to the magnetic field

The electric force acts on a charged particle independent of the particle’s velocity, but the magnetic force acts on a charged particle only when it is in motion

The electric force can change the speed of a charged particle while the magnetic force associated with a steady magnetic field changes the direction of the particle, but not its speed

Concept Test #1What direction is the force this wire feels because of the magnetic field?

1) To the right

2) To the left

3) Up the page

4) Down the page

5) Into the page

6) Out of the pageCurrent I

Magnetic Field B

Magnetic Force on a Current

sinqvBF

sinB

L

tv

I

t

qF

sinILBF angle between I and B

Torque on a Current-Carrying Coil

The two forces on the loop have equal magnitude but they are opposite in direction.

Concept Test #2A square loop carries a current I and pivots without friction about the z-axis. A uniform magnetic field B points in the +x direction, and the loop initially makes an angle θ with the x-z plane. The torque on the loop is clockwise.

True (yes) False (no)

Calculate the Torque

sinsin

sin

21

21

IABwILB

wILB

sin

momentmagnetic

BNIA N = number of turns of wire

"" ckwisecounterclo

""clockwise :Direction

sin :Recall Fr

Max and Min Torques

The loop tends to rotate such that its normal becomes aligned with the magnetic field

Origins of Magnetic Fields Magnetic fields come from:

• Magnets• Moving charges (i.e. currents)• Changing E fields (more next lecture…)

Magnetic field lines never end; they must form closed loops

No magnetic charges (monopoles) exist

B produced by a long straight wire

r

IB o

2

AmT104 7 o

permeability of free space

Increases with current, falls off with distance

Direction of B field of a straight wire The magnetic field

due to the current in a long straight wire has circular field lines around the wire

The direction of the

field is given by the right hand rule

Concept Test #3Two identical parallel long straight wires carrying a current I stand a distance r apart. Which of the following statements is false?

1) The magnetic field B created by the bottom wire at P points out of the page.

2) The force exerted by the bottom wire on the top wire is F = ILB.

3) The force pushes the top wire up.

F

P

I

I

L

r

r

IB oP

2

r

IL

r

IILF oo

22

2

Concept Test #4Two parallel long straight wires carrying currents I and 2I stand a distance r apart. Which of the following statements is false?

1) The magnetic force pulls the top wire down toward the bottom wire.

2) The magnetic force pulls the bottom wire up toward the top wire.

3) The magnetic force on the top wire is greater than the magnetic force on the bottom wire.

P

I

2I

L

F r

the two wires generate magnetic fields that pull one another toward each other Newton’s 3rd Law.

r

ILF o

2

2 2

21

The force is attractive if the currents are in the same direction and repulsive otherwise

Electromagnet Current flowing in a loop of wire creates a

magnetic field Current loop can be imagined to be a phantom bar

magnet

=

http://www.windows.ucar.edu/spaceweather/info_mag_fields.html

Right hand rule

Which side is north pole?

N

S

At center of circular loop

R

INB o

2

number of turns

B produced by a solenoid

Interior of a solenoid

nIB onumber of turns per unit length

Ampere’s Law Ampere’s law relates sum of

B field along a line to current inside

Formally:

IB o ||

net current passing through surface bounded by path

B field of wire from Ampere’s Law

IB o

IrB o 2

IB o ||

r

IB o

2

Same as before!

=

N

S