General Physics II, Lec 11, Discussion, By/ T.A. Eleyan 1 Review (Electrostatic)

General Physics II, Lec 11, Discussion, By/ T.A. Eleyan

1

Review

(Electrostatic)


2

[1] Three charges are located in the XY plane as Shown in the figure. Q1= - 3 nC, Q2 = 5 nC Q3 = 3 nC. The distance between Q1 and Q2 is

8 m and between Q2 and Q3 is 6 m.

Find: a)The electric field due to the charges at the origin O.b)The electric potential due to these charges at the origin O.c) What is the direction of the net force on the point O.


3

a)The electric field due to the charges at the origin O.

CNEEE

CN

EEEE

CN

EEEE

CNE

CNE

CNE

yxT

x

x

/3.10

/2.05

3

25

27

5

3

25

27

5

3

5

9

sinsinsin

/2.35

4

25

27

5

4

5

9

5

4

25

27

coscoscos

/25

27

25

103109

/5

9

25

105109

/25

27

25

103109

22

232122

232221

99

3

99

2

99

1


4

VVVVV

VV

VV

VV

95

27

5

103109

95

105109

5

27

5

103109

321

99

3

99

2

99

1

06.18006.0180

0625.02.3

2.0tan

EofdirectiontheisforcenettheofdirectionThe

x

y

E

E

b) The electric potential due to these charges at the origin O.

c) What is the direction of the net force on the point O.


5

[2] Two point charges are located on the x-axis as follows: charge Q1 = 8x10-9 C is at x = 0 and charge Q2 = -1x10-9 C is at x = 1cm. What is the net force in the x direction on a third charge,Q3 = +2x10-9

C, placed at x = 2 cm ?

NF

directionxveinNcm

kF

directionxveinNcm

kF

net4

42

99

2

42

99

1

108.1

108.1)2(

101102

106.3)2(

108102

lawscoulomb'using


6

]3 [In a hydrogen atom an electron circles a proton. Since the mass of the proton is much greater than the mass an electron, assume that the proton stays fixed in space and the electron rotates around it

with radius 0.529x10-10 m. What is the velocity of the electron?

smmr

kev

r

ke

r

mvF

/102.2

iselectrontheonforceThe

62

2

22


7

]4 [A uniform electric field exists in the region between two oppositely charged plane parallel plates. An electron is released from rest at the surface of the negatively charged plate and strikes the surface of the opposite plate 2x10-8 s later. If the magnitude of the electric

field is 4x103 N/C, what is the separation between the plates?

cmatd

smmr

kev

smm

eE

m

Fa

142

1

restfromstartselectrontheSince

/102.2

/107

onacceleraticonstantinvolvingproblemisThis

2

62

214


8

]5 [Two charged particles are placed on the x-axis as follows: Q1 = 1x10-9 C at x = 0 m and Q2 = -2x10-9 C at x = 1.6 m. Where on the x-axis is

the electric field zero?

The electric field can only be zero where the field due to Q1 and Q2 point in opposite direction. This occurs both for x<0m and for x>1.6 m, however since Q2 is greater in magnitude, one must be further away from it in order to have the magnitudes of the fields due to Q1 and Q2 be equal. This means the field is

zero in the region x<0 .

Sitting the magnitude equal,

mxormx

xx

xx

x

Qk

x

Qk

66.086.3

26.1

2)6.1(

)6.1()(22

22

21


9

[6 ]Two stationary point charges are arranged on the x-axis as follows: Q1 = 2.4x10-10 C at x = 0 m and Q2 = -1.2x10-10 C at x = 1 m. An electron is placed at x = 2 m and let go. What is the velocity of the electron when it reaches x = 3 m.

smv /105.2 5

This is a conservation of energy problem. The initial kinetic energy of the electron is zero. The initial and final potential energy of the electron are:

Consequently, the final kinetic energy is

And the final velocity of the electron is

Jqkqqkq

PE

Jqkqqkq

PE

eef

eei

2021

21

1088.223

012

JPEPEkkvm fiiffe202 1088.2

2

1


10

[7 ]Using the superposition principle determine the electric field at point P in Fig.

mVEp /02

101

2

102

2

103

0

9

0

9

0

9

Using the convention that a positive electric field is up and a negative electric field is down, the net electric field at p is


11

[8] A 1 Coulomb charge is located at the origin. Another charge, Q, is located at x = 3 m. If the electric field is zero at x = 1 m, what is Q?

The electric field due to the 1C charge is in positive x-direction at x=1m. In order to cancel this field, the charge at x=3m must be positive so that its electric field is in the negative x-direction at x=1m. The two field will cancel if they have the same magnitude.

CQkQk

4)2()1(

)1(22


12

V

C1

C2

+-

C3

C1 = 10 F

C2 = 5.0 F

C3 = 4.0 F

[9]

a) Find the equivalent capacitance of the entire combination.

C1 and C2 are in series.

21

2112

2112

111

CC

CCC

CCC

FC 3.315

50

510

51012

C12 and C3 are in parallel.

FCCCeq 3.70.43.3312


13

b) If V = 100 volts, what is the charge Q3 on C3?

C = Q/V

100100.4 633 VCQ

c) What is the total energy stored in the circuit?

CoulombsQ 43 100.4

JVCU eq2462 106.310103.1

2

1

2

1

JU 2106.3


14

]10 [A wire of uniform charge density and length L lies along the x

axis as shown in Figure. What is the electric potential at point A?

x

dxk

x

dqkdV

dxdq

ee

dlde

dl

d

e

dl

d

e xkx

dxk

x

dxkV

ln

)/1ln(ln)ln( dlkddlkV ee


15

[11] Determine the point nearest the charges where the total electric field is zero. Take the -2.50 µC charge to be at the origin of the x

axis.

-6.00 C-2.50 C

1.00 m

0.39 m

[12] The plates of a parallel plate capacitor are separated by 1 x 10–4 m. If the material in between them is a jelly with a dielectric constant

of 2.26, what is the plate area needed to provide a capacitance of 1.50 pF?

7.50 x 10-6 m2


16

[13] Find the charge on the 2 F capacitor in the following circuit.

[14] Each of the protons in a particle beam has a kinetic energy of 3.25x10-15 J What are the magnitude and direction of the electric

field that will stop these protons in a distance of 1.25 m?

1.63 x 104 N/C and opposite to the motion

2 F 4 F

2 F

12 V

18µC


17

]15 [Three point charges are fixed on the corners of an equilateral triangle whose one side is b as shown in Figure.

1 .What is the magnitude of the Coulomb force acting on charge –q due to presence of other

charges?

2 .What is the value of the electric potential at the center (point A) of positive charges?

3 .What is the electric potential energy of system?

2

2

3b

qk

b

qk)

3

14(

b

qk

2


18

]16 [The stored energy of a capacitor is 3.0 J after having been charged by a 1.5 V battery. What is the energy of the capacitor after it is

charged by 3.0 V battery ?

J12

FCeq 9.257

57

]17 [Find the equivalent capacitance between points a and b in the combination of capacitors shown in Figure.

7µF and 5µF series

4µF, 6µF and 2.9µF parallel

FCeq 9.129.264


19

[18 ]Two capacitors when connected in parallel give an equivalent capacitance of 9.00 pF and give an equivalent capacitance of 2.00 pF

when connected in series. What is the capacitance of each capacitor?

)1.........(..........921 CC

)2.........(..........221

21 CC

CC

in parallel

in series

Solve eq.1&2

pFCpFCor

pFCpFC

3,6,

6,3

21

21

General Physics II, Lec 11, Discussion, By/ T.A. Eleyan 1 Review (Electrostatic)

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Transcript of General Physics II, Lec 11, Discussion, By/ T.A. Eleyan 1 Review (Electrostatic)