Chapter 17 Electric Fields (A2)

CAMBRIDGE A LEVELPHYSICS

CAMBRIDGE A LEVELPHYSICS

ELECTRIC FIELDS(A2)

ELECTRIC FIELDS(A2)

LEARNING OUTCOMESLEARNING OUTCOMESNUMBER LEARNING OUTCOME

i Un d e r s t a n d C o u l omb s L awii. L e a r n a b o u t e l e c t r i c f i e l d s a r o u n d p o i n t c h a r g e s

a n d h ow t o c a l c u l a t e t h e e l e c t r i c f i e l d s t r e n g t h a ta p o i n t

ii Wha t i s m e a n t b y t h e t e rm e l e c t r i c p o t e n t i a l ?iii Un d e r s t a n d t h e r e l a t i o n s h i p b e twe e n t h e

p o t e n t i a l g r a d i e n t a n d e l e c t r i c f i e l d s t r e n g t h , a n de l e c t r i c f o r c e

iv L o o k a t t h e s im i l a r i t i e s a n d d i f f e r e n c e s b e twe e ne l e c t r i c f i e l d s a n d g r a v i t a t i o n a l f i e l d s

COULOMBS LAWCOULOMBS LAW Charged particles are capable ofexerting an electric force on oneanother. Like charges repel each other, whileunlike charges attract each other. We can use Coulombs Law to calculatethe magnitude of the electric force thatone charged particle exerts on another. Coulombs Law is applicable only whenthe two charges are in free space or air.

Charged particles are capable ofexerting an electric force on oneanother. Like charges repel each other, whileunlike charges attract each other. We can use Coulombs Law to calculatethe magnitude of the electric force thatone charged particle exerts on another. Coulombs Law is applicable only whenthe two charges are in free space or air.

COULOMBS LAWCOULOMBS LAW Coulombs Law states that the electricforce that a charged particle exerts onanother charged particle is directlyproportional to the product of theircharges and inversely proportional tothe square of their distance ofseparation. The direction of this electricforce is also along the line joining theseparticles.

Coulombs Law states that the electricforce that a charged particle exerts onanother charged particle is directlyproportional to the product of theircharges and inversely proportional tothe square of their distance ofseparation. The direction of this electricforce is also along the line joining theseparticles.

COULOMBS LAWCOULOMBS LAW Mathematically, the electric force, F isgiven by = where= = .

and are the magnitude of the pointcharges, in C and is the separationbetween the point charges, m. is known as the relative permittivity offree space and has a value of 8.85 10 .

Mathematically, the electric force, F isgiven by = where= = .

and are the magnitude of the pointcharges, in C and is the separationbetween the point charges, m. is known as the relative permittivity offree space and has a value of 8.85 10 .

COULOMBS LAWCOULOMBS LAW The direction of the force wouldbe along the line joining bothcharges and would:

point away from both charges if bothcharges have the same (repulsive),andtowards both charges if they haveopposite signs (attractive).

The direction of the force wouldbe along the line joining bothcharges and would:point away from both charges if bothcharges have the same (repulsive),andtowards both charges if they haveopposite signs (attractive).

COULOMBS LAWCOULOMBS LAW

Examples 21.1 and 21.2, pages 696 and 697, Sears and Zemanskys UniversityPhysics, Young and Freedman, 13th edition, Pearson Education, San Francisco, 2012.

ELECTR IC F I E LDS AROUNDCHARGED PART IC LES

E LECTR IC F I E LDS AROUNDCHARGED PART IC LES

Electric fields exist around everycharged particle. To find out how the electric fieldaround a charged particles look, weuse two fundamental charges,positive and negative point chargesand look at the direction of forcesthey exert on a positive test charge.

Electric fields exist around everycharged particle. To find out how the electric fieldaround a charged particles look, weuse two fundamental charges,positive and negative point chargesand look at the direction of forcesthey exert on a positive test charge.



We place the positive test chargearound the positive charge.

The arrows show the direction ofthe force that the positive chargewill exert on the positive testcharge (repulsive).

Two points to note:I. The direction of the arrows,

all away from the positivecharge.

II. The lengths of the arrowsdecrease as the distance fromthe charge increases.

Diagram 21.18(a), page 701, Sears and ZemanskysUniversity Physics, Young and Freedman, 13th edition,Pearson Education, San Francisco, 2012.



If we draw more vectors, andconnect the heads and tails ofvectors that radially adjacent,we obtain the shape as seenon the diagram on the left.

These lines around thepositive point charge areknown as the electric fieldlines.

Source:http://demo.webassign.net/ebooks/cj6demo/art/images/c18/nw0736-n.gif.



The field lines are radiallysymmetrical, and arespaced further apart as wemove away from thecharge, and are directedaway from the positivecharge.

Source: http://demo.webassign.net/ebooks/cj6demo/art/images/c18/nw0736-n.gif.



We place the positive test chargearound the negative charge.

The arrows show the direction ofthe force that the negative chargewill exert on the positive testcharge (attractive).

Two points to note:I. The direction of the arrows,

all towards the negativecharge.

II. The lengths of the arrowsdecrease as the distance fromthe charge increases.

Diagram 21.18(b), page 701, Sears and ZemanskysUniversity Physics, Young and Freedman, 13th edition,Pearson Education, San Francisco, 2012.



If we draw more vectors, andconnect the heads and tails ofvectors that radially adjacent,we obtain the shape as seenon the diagram on the left.

These lines around thenegative point charge areknown as the electric fieldlines.

Source:http://demo.webassign.net/ebooks/cj6demo/art/images/c18/nw0737-n.gif



The field lines are radiallysymmetrical, and arespaced further apart aswe move away from thecharge, and are directedtowards the negativecharge.

Source: http://demo.webassign.net/ebooks/cj6demo/art/images/c18/nw0737-n.gif



The electric field strength, E at apoint in space is defined as themagnitude of electric force actingon per unit of positive test charge. We can use Coulombs Law and thedefinition of the E field strength at apoint to derive an equation for the E field strength.

The electric field strength, E at apoint in space is defined as themagnitude of electric force actingon per unit of positive test charge. We can use Coulombs Law and thedefinition of the E field strength at apoint to derive an equation for the E field strength.



For a field around a point charge(positive or negative) in free space,we can use Coulombs Law to derive= . Units of E is / . =magnitude of the point charge,C and = distance between thepoint charge and the point, m. For a field around a point charge(positive or negative) in free space,we can use Coulombs Law to derive= . Units of E is / . =magnitude of the point charge,C and = distance between thepoint charge and the point, m.



The direction of the electric fieldwould be along the line joining thecharge and point and: away from the charge if the charge ispositive,towards the charge if the charge isnegative.

The direction of the electric fieldwould be along the line joining thecharge and point and: away from the charge if the charge ispositive,towards the charge if the charge isnegative.



Examples 21.5 and Exercise 21.26, pages 701 and 716, Sears and ZemanskysUniversity Physics, Young and Freedman, 13th edition, Pearson Education, SanFrancisco, 2012.

ELECTRIC POTENTIALELECTRIC POTENTIAL The electric potential, at point inspace is defined as the work done inbringing per unit of positive chargefrom infinity to that point. In equation form, = = The units of V is J C-1 .

The electric potential, at point inspace is defined as the work done inbringing per unit of positive chargefrom infinity to that point. In equation form, = = The units of V is J C-1 .

ELECTRIC POTENTIALELECTRIC POTENTIALA few points to note: The sign of the electric potentialaround a point charge depends on thesign of the charge. It will be positive ifthe point charge is positive, andnegative if the charge is negative. The electric potential increases if thepoint is nearer to a positive pointcharge. The electric potential decreases if thepoint is nearer to a negative pointcharge.

A few points to note: The sign of the electric potentialaround a point charge depends on thesign of the charge. It will be positive ifthe point charge is positive, andnegative if the charge is negative. The electric potential increases if thepoint is nearer to a positive pointcharge. The electric potential decreases if thepoint is nearer to a negative pointcharge.

ELECTRIC POTENTIALELECTRIC POTENTIALA few points to note (contd): If the electric potential at a point isdue to more than one point charge,we find the algebraic sum of theelectric potential due to theindividual point charges. The electric potential, = A few points to note (contd): If the electric potential at a point isdue to more than one point charge,we find the algebraic sum of theelectric potential due to theindividual point charges. The electric potential, =

ELECTRIC POTENTIALELECTRIC POTENTIAL

Example 23.3, page 764, Sears and Zemanskys University Physics, Young andFreedman, 13th edition, Pearson Education, San Francisco, 2012.


Example 23.4, page 765, Sears andZemanskys University Physics, Young andFreedman, 13th edition, Pearson Education,San Francisco, 2012.

ELECTRIC POTENTIALELECTRIC POTENTIAL How do we relate electric potential, V toelectric potential energy, U?

We can calculate the U of a charge placed inan electric field by using = where q =magnitude of the charged particle, in C.

Note that a change in potential results in achange in potential energy; i.e. work done byor against the electric field.

How do we relate electric potential, V toelectric potential energy, U?

We can calculate the U of a charge placed inan electric field by using = where q =magnitude of the charged particle, in C.

Note that a change in potential results in achange in potential energy; i.e. work done byor against the electric field.


Example 23.5, page 766, Sears and Zemanskys University Physics, Young andFreedman, 13th edition, Pearson Education, San Francisco, 2012.


Exercise 23.19, page 780, Sears and Zemanskys University Physics, Young andFreedman, 13th edition, Pearson Education, San Francisco, 2012.

POTENTIAL GRADIENTPOTENTIAL GRADIENT The potential gradient is the derivative of theelectric potential function, ( ).

The negative of the potential gradient at apoint gives the magnitude of the electric fieldstrength, at that particular point.

Mathematically, = . This equation isnot necessary to be remembered.

The potential gradient is the derivative of theelectric potential function, ( ).

The negative of the potential gradient at apoint gives the magnitude of the electric fieldstrength, at that particular point.

Mathematically, = . This equation isnot necessary to be remembered.

POTENTIAL GRADIENTPOTENTIAL GRADIENT Let us analyse the potential for a positivepoint charge. This function is = . Let us analyse the potential for a positivepoint charge. This function is = .

Where is the gradienthighest?

Where is the gradientlowest?

What does the two answersabove tell us about the E field strength around apositive point charge?

GRAV ITAT IONAL F I E LDS v s .E LECTR IC F I E LDS




Gravitational field Electric fieldPotential in a radial field =

Units : J kg-1ScalarAlways negative (

EXAMPLESEXAMPLESMay/Jun 2008, Paper 4, Question 4.May/Jun 2008, Paper 4, Question 4.

EXAMPLESEXAMPLESMay/Jun 2008, Paper 4, Question 4 (contd).May/Jun 2008, Paper 4, Question 4 (contd).

HOMEWORKHOMEWORK1. Winter 09, Paper 41, question 5.2. Summer 10, Paper 41, question 4.3. Summer 11, Paper 41, question 1.4. Summer 11, Paper 41, question 1.5. Winter 11, Paper 41, question 4.

1. Winter 09, Paper 41, question 5.2. Summer 10, Paper 41, question 4.3. Summer 11, Paper 41, question 1.4. Summer 11, Paper 41, question 1.5. Winter 11, Paper 41, question 4.

Documents

Chapter 17 Electric Fields (A2)