Electrical energy

potential difference and electric potential

energy conservation

electric potential of point charges

problems electrostatic force

problem in electric field

problem in electric flux

Assignments: For next class: Finish reading Ch 20 HW4 Set due next Wed, 9/18

Question/Observation Mondays

Research Q/O with HW (Wednesday)

Exam # 1 (Wednesday, 9/25 )

Assignments: For next class: finish reading Ch 20 HW4 Set due next Thursday, 9/19

Question/Observation Tuesday

Research Q/O with HW (Thursday)

If the surface is not perpendicular to

the field, the expression of the field

becomes:

4

cosEA

N

The work done by a conservative force equals the negative of the change in potential energy, DPE

This equation is valid only for the case of a uniform electric field

allows to introduce the concept of electric potential

9/15/2013 5

EdqWU 0D

The potential difference between points A and B, VB-VA, is defined as the change in potential energy (final minus initial value) of a charge, q, moved from A to B, divided by the charge

Electric potential is a scalar quantity Electric potential difference is a measure

of electric energy per unit charge Potential is often referred to as “voltage”

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00 q

W

q

UVVV AB

DD

Electric potential difference is the work done to move a charge from a point A to a point B divided by the magnitude of the charge. Thus the SI units of electric potential

In other words, 1 J of work is required to move a 1 C of charge between two points that are at potential difference of 1 V

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1 1V J C

Electron volt (eV) is more convenient

and commonly used unit.

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JXVCXeV 1919 1060.1)1)(1060.1(1

A uniform electric field of magnitude 6.8 X 105 N/C points in the positive x direction. Find the change in electric potential energy of a 2.5 uC charge as it moves from the origin to the points (a) (0, 4.0 m ); (b) (4,0 m, 0) ; and ( c ) ( 4,0 m , 4, 0 m )

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The potential difference between points A and B, VB-VA, is defined as the change in potential energy (final minus initial value) of a charge, q, moved from A to B, divided by the charge

Electric potential is a scalar quantity Electric potential difference is a measure

of electric energy per unit charge Potential is often referred to as “voltage”

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B A

PEV V V

q

DD

The work done by the electric field is the

magnitude of the electric force, F = q E, times the

distance, ∆s:

Therefore, the change in electric potential is:

Connection E and EP

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sEqW D 0

sEq

SEq

q

WV D

D

D

0

0

0

)(

s

VE

D

D

Units of electric field (N/C) can be expressed in terms of the units of potential (as volts per meter)

Because the positive tends to move in the direction of the electric field, work must be done on the charge to move it in the direction, opposite the field. Thus, • A positive charge gains electric potential energy when

it is moved in a direction opposite the electric field • A negative charge looses electrical potential energy

when it moves in the direction opposite the electric field

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1 1N C V m

A parallel-plate capacitor has plates

separated by 0.035 in. If and electric field

of 4.0 x 106 V/m is between them. (a) Find

the potential difference? (b) If the

separation between the plates decreased,

does the required potential difference

increase, decrease or stay the same?

Explain. ( c ) Find the potential difference

for a separation of 0.55mm.

9/15/2013

13

The same kinetic-potential energy theorem works here

If a positive charge is released from A, it accelerates in the direction of electric field, i.e. gains kinetic energy

If a negative charge is released from A, it accelerates in the direction opposite the electric field

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A

B

q d

A

B

m d

E g

i i f fKE PE KE PE

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Vab

What is the speed of an electron accelerated from rest across a potential difference of 100V? What is the speed of a proton accelerated under the same conditions?

Given: DV=100 V me = 9.1110-31 kg mp = 1.6710-27 kg |e| = 1.6010-19 C Find: ve=? vp=?

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Observations: 1. given potential energy difference, one can find the

kinetic energy difference 2. kinetic energy is related to speed

i i f fKE PE KE PE

f i fKE KE KE PE q V D D

21 2

2f f

q Vmv q V v

m

D D

Electric circuits: point of zero potential is defined by grounding some point in the circuit

Electric potential due to a point charge at a point in space: point of zero potential is taken at an infinite distance from the charge

With this choice, a potential can be found as

Note: the potential depends only on charge of an object, q, and a distance from this object to a point in space, r.

Si unit: volt, V

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e

qV k

r

Consider a system of two particles If V1 is the electric potential due to charge q1 at a

point P, then work required to bring the charge q2 from infinity to P without acceleration is q2V1. If a distance between P and q1 is r, then by definition

Potential energy is positive if charges are of the same sign and vice versa.

SI unit: joule, J

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P A

q1 q2

r

1 22 1 e

q qPE q V k

r

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20 9/15/2013

Find the electric flux through the area

A = 2 m2, which is perpendicular to an

electric field E=22 N/C

EA

21 9/15/2013

A surface encloses the charges

q1 = -3u C, q2 = 2uC and q3= -4 uC. Find

the electric flux.

EA

insideQ

22

Example 6:

q1 = 12.00 uC q2 = -10.00 uC q3 = 25.00 uC d1 = 9.00 cm d2 = 6.00 cm K = 8.99 x 109 N.m2 /C2

Find the direction and magnitude of the net electrostatic force exerted on the point q2.

Find the direction and magnitude on the net electrostatic force exerted on the point charge Q2.

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2

1

3

4

Q1 = - 24 u C Q2 = 36 u C Q3 = 12 u C Q4 = 42 u C d = 40 cm

Example 7

insideE

o

Q

Ll joule/C = volt, V volts/meter, V/m Energy Conservation: K1 + U1 = K2 + U2 F l

00 q

W

q

UVVV AB

DD

s

VE

D

D 2e

qE k

r