Electric and Electric and Magnetic FieldsMagnetic Fields

Chapters 17 & 21Chapters 17 & 21

Electric FieldElectric Field Electric force, like gravitational Electric force, like gravitational

force, is a field forceforce, is a field force Remember: Field forces can act through Remember: Field forces can act through

space even when there is no physical space even when there is no physical contact between the objects involvedcontact between the objects involved

A charged object has an electric field A charged object has an electric field in the space around itin the space around it

Electric Field LinesElectric Field Lines Electric Field Lines point in the Electric Field Lines point in the

direction of the electric fielddirection of the electric field

The number and spacing of field lines The number and spacing of field lines is proportional to the electric field is proportional to the electric field strengthstrength The electric field is strong where the The electric field is strong where the

field lines are close together and weaker field lines are close together and weaker when they are far apartwhen they are far apart

Electric Field LinesElectric Field Lines The lines for a positive charge point The lines for a positive charge point

away from the chargeaway from the charge

The lines for a negative charge point The lines for a negative charge point towards the chargetowards the charge

Electric Field LinesElectric Field Lines This diagram shows the electric field This diagram shows the electric field

lines for two equal and opposite lines for two equal and opposite point chargespoint charges Notice that the lines begin on the Notice that the lines begin on the

positive charge and end on the negative positive charge and end on the negative chargecharge

Electric Field LinesElectric Field Lines This diagram shows the electric field This diagram shows the electric field

lines for two positive point chargeslines for two positive point charges Notice that the same number of lines Notice that the same number of lines

emerges from each charge because emerges from each charge because they are equal in magnitudethey are equal in magnitude

Electric Field LinesElectric Field Lines If the charges are unequal, then the If the charges are unequal, then the

number of lines emerging from them number of lines emerging from them will be differentwill be different Notice that the positive charge has Notice that the positive charge has

twice as many linestwice as many lines

Calculating Electric Field Calculating Electric Field StrengthStrength

The equation for the electric field The equation for the electric field produced by a point charge is:produced by a point charge is:

KKcc=9x10=9x1099 Nm Nm22/C/C22 ,r is the distance from the charge and q is ,r is the distance from the charge and q is the charge producing the fieldthe charge producing the field

The unit for E is N/CThe unit for E is N/C

Electric field strength is a vector!!Electric field strength is a vector!! If q is positive, then E is directed away If q is positive, then E is directed away

from qfrom q If q is negative, then E is directed toward qIf q is negative, then E is directed toward q

2rqkE c

Calculating the force from an Calculating the force from an electric fieldelectric field

If a charged object is placed in an If a charged object is placed in an electric field, we can calculate the electric field, we can calculate the force acting on it from the electric force acting on it from the electric fieldfield

Remember that F is a vector!! Remember that F is a vector!!

F qE

Sample Problem p. 647 Sample Problem p. 647 #3#3

An electric field of 2.0 x 10An electric field of 2.0 x 1044 N/C is N/C is directed along the positive x-axisdirected along the positive x-axis

a. What is the electric force on an a. What is the electric force on an electron in this field?electron in this field?

b. What is the electric force on a b. What is the electric force on a proton in this field?proton in this field?

Sample Problem p. 647 Sample Problem p. 647 #3#3

E= 2.0 x 10E= 2.0 x 1044 N/C , q= 1.6 x 10 N/C , q= 1.6 x 10-19-19 C C F=qE= 3.2 x 10F=qE= 3.2 x 10-15-15 N for both the N for both the

electron and the protonelectron and the proton

What about the direction?What about the direction? The electric field is pointing along the The electric field is pointing along the

positive x axis (to the right) which positive x axis (to the right) which means there’s a positive charge to the means there’s a positive charge to the left left

E field+

For the protonFor the proton Since the electric field is pointing to Since the electric field is pointing to

the right, if you put a proton in it, the the right, if you put a proton in it, the proton will want to move away towards proton will want to move away towards the right and the direction of the force the right and the direction of the force on it will be to the righton it will be to the right

Answer: 3.2 x 10Answer: 3.2 x 10-15-15 N along the positive N along the positive x axis (to the right)x axis (to the right)

+ +F

For the electronFor the electron Since there’s a positive charge causing Since there’s a positive charge causing

the electric field to point towards the the electric field to point towards the right, an electron would feel attracted right, an electron would feel attracted to the positive charge. Therefore, the to the positive charge. Therefore, the force acting on it is toward the leftforce acting on it is toward the left

Answer: 3.2 x 10Answer: 3.2 x 10-15-15 N along the N along the negative x axis (to the left)negative x axis (to the left)

+ -F

Sample Problem p. 656 Sample Problem p. 656 #38#38

Find the electric field at a point midway Find the electric field at a point midway between two charges of +30 nC and 60 nC between two charges of +30 nC and 60 nC separated by a distance of 30.0 cmseparated by a distance of 30.0 cm

+30 nC +60 nC

Sample Problem p. 656 Sample Problem p. 656 #38#38

For the 30 nC charge:For the 30 nC charge:

Direction of the E-field for both charges is Direction of the E-field for both charges is “away” since they’re both positive“away” since they’re both positive

For the 60 nC For the 60 nC charge:charge:

+30 nC +60 nC

C

Nmxx

rqkE c 000,12

15.0)1030(109

2

99

2

CN

mxx

rqkE c 000,24

15.0)1060(109

2

99

2

Which one will win?Which one will win? At the midway point, the 30nC charge’s field At the midway point, the 30nC charge’s field

strength is 12000 N/C toward the 60 nC strength is 12000 N/C toward the 60 nC charge and the 60 nC charge’s field strength charge and the 60 nC charge’s field strength is 24,000 N/C toward the 30 nC charge.is 24,000 N/C toward the 30 nC charge.

The 60 nC charge will win. Since the field’s The 60 nC charge will win. Since the field’s point in opposite directions, you have to point in opposite directions, you have to subtractsubtract

Answer: 12,000 N/C toward the 30 nC chargeAnswer: 12,000 N/C toward the 30 nC charge

Sample Problem (p.659 Sample Problem (p.659 #66)#66)

A constant electric field directed A constant electric field directed along the positive x-axis has a along the positive x-axis has a strength of 2.0 x 10strength of 2.0 x 1033 N/C. N/C. Find the electric force exerted on a Find the electric force exerted on a

proton by the fieldproton by the field Find the acceleration of the protonFind the acceleration of the proton

Answer Answer F=qE=(1.6x10F=qE=(1.6x10-19-19 C)(2.0 x 10 C)(2.0 x 1033 N/C)= N/C)=

3.2 x 103.2 x 10-16-16 N N

Direction?Direction?

Answer: 3.2 x 10Answer: 3.2 x 10-16-16 N along the positive x-axis N along the positive x-axis (to the right)(to the right)

E field+ +

F

Answer Answer B. What is the acceleration?B. What is the acceleration?

Ask Newton!Ask Newton! F=maF=ma a = F/m= 3.2 x 10a = F/m= 3.2 x 10-16-16 N/1.6x10 N/1.6x10-27-27 kg kg a= 2 x 10a= 2 x 101111 m/s m/s22 along the positive x along the positive x

axisaxis

Magnetism!Magnetism!

MagnetsMagnets The ends of a bar magnet are called The ends of a bar magnet are called

polespoles Like poles repel and unlike poles attractLike poles repel and unlike poles attract Regardless of their shape, all magnets Regardless of their shape, all magnets

have a north and south polehave a north and south pole

Magnetic FieldsMagnetic Fields Magnetic Field lines point from the Magnetic Field lines point from the

north pole to the south pole of the north pole to the south pole of the magnetmagnet The north pole of a compass needle The north pole of a compass needle

always points in the direction of the always points in the direction of the field (from North to South)field (from North to South)

Magnetic Field of the Magnetic Field of the EarthEarth

The Earth’s geographic North pole is The Earth’s geographic North pole is actually the magnetic south poleactually the magnetic south pole The north pole of a compass points The north pole of a compass points

towards geographic north and since towards geographic north and since opposites attract, we know that the opposites attract, we know that the Earth’s geographic pole is magnetic Earth’s geographic pole is magnetic southsouth

Magnetic Field of a wireMagnetic Field of a wire

Moving charges Moving charges produce magnetic produce magnetic fieldsfields

If there is a current If there is a current moving through a moving through a wire, a magnetic wire, a magnetic field is produced field is produced around the wirearound the wire

Magnetic Field of a wireMagnetic Field of a wire

The “Right Hand Rule” for the The “Right Hand Rule” for the magnetic fieldmagnetic field

Point your thumb in the direction of Point your thumb in the direction of the current and curl your fingers in the current and curl your fingers in the direction of the fieldthe direction of the field

Magnetic Force Magnetic Force A charge moving through a magnetic A charge moving through a magnetic

field experiences a forcefield experiences a force

q= magnitude of chargeq= magnitude of chargev= speed of chargev= speed of chargeB= Strength of the magnetic field (measured B= Strength of the magnetic field (measured

in Tesla, T)in Tesla, T)

qvBFmagnetic

A second Right-Hand A second Right-Hand RuleRule

Of course, force is a vector!Of course, force is a vector!

To find the direction of the magnetic To find the direction of the magnetic force use another right hand ruleforce use another right hand rule Fingers point in direction of the fieldFingers point in direction of the field Thumb points in direction of vThumb points in direction of v Palm points in direction of magnetic Palm points in direction of magnetic

forceforce

Conventions for Conventions for direction of fielddirection of field

Direction of Field

Symbol

Into the page

X

Out of the page

WARNING: The right hand rule is for thedirection of the force acting on a POSITIVE CHARGE.

To find the direction of the force acting on a negative charge, you’ll have to use the rule and change the sign!

ExamplesExamplesDirection of F Direction of v Direction of B Sign of Charge

Out of the page East North +

Into the page East North -

Out of the page West South +

Into the page West South -

South West Into the page +

South West Out of the page -

East North Out of the page +

South Out of the page East -

Out of the page South West -

Into the page west North +

Sample Problem p. 775 Sample Problem p. 775 #2#2(edited)(edited)

A proton traveling to the right along A proton traveling to the right along the x-axis enters a region where the x-axis enters a region where there is a magnetic field of 2.5 T there is a magnetic field of 2.5 T directed north. If the proton directed north. If the proton experiences a force of 3.2 x 10experiences a force of 3.2 x 10-12-12 N, N, find the speed of the proton. What is find the speed of the proton. What is the direction of the force exerted on the direction of the force exerted on the proton?the proton?

The speed of the protonThe speed of the proton

What’s the direction of F? Use the What’s the direction of F? Use the RHR!!RHR!! v is east, B is north…F is….v is east, B is north…F is…. Out of the page!Out of the page! If it was an electron, the force would be If it was an electron, the force would be

into the page!into the page!

smx

TCxNx

qBF

v magnetic 619

12

100.8)5.2)(106.1(

102.3

Sample Problem (not in Sample Problem (not in book)book)

An electron is moving with a velocity An electron is moving with a velocity of 6 x 10of 6 x 1066 m/s westward in a 3.0 T m/s westward in a 3.0 T magnetic field that is pointed out of magnetic field that is pointed out of the page.the page. Find the magnitude and direction of the Find the magnitude and direction of the

force acting on the electron.force acting on the electron.

Sample Problem (not in Sample Problem (not in book)book)

F= 2.88 x 10F= 2.88 x 10-12-12 N N Direction? Use the RHRDirection? Use the RHR

V points west, B points out of the page…V points west, B points out of the page…

F points SOUTH (remember it’s an F points SOUTH (remember it’s an electron!!)electron!!)

)0.3)(106)(106.1( 619 TsmxCxqvBFmagnetic