PHYSICS ~ CAPE LEVEL HAMPTON SCHOOL

E-FIELDS and B-FIELDS (Electric Fields & Capacitance)

Teacher: G. David Boswell Date: November 01, 2018 Time Span: 01:00 p.m. to 02:30 p.m. Duration: 90 Mins

STUDENT: ____________________ ____________________ GRADE: ______ SURNAME FIRSTNAME

1. The standard units of electric field intensity, , are

(A) (B) (C) (D)

2. Electric field intensity, , can also be expressed in the units of

(A) (B) (C) (D)

3. Let k denote coulomb’s constant. The magnitude of the electric field at a distance r from an isolated point particle with charge q is:

(A)

(B)

(C)

(D)

4. Let k denote coulomb’s constant. The magnitude of the electric force on a charge at a distance from an isolated point particle with charge Q is:

(A)

(B)

(C)

(D)

5. The magnitude of the electric field at a distance d from the center of a hollow charged isolated sphere of radius r, where is

(A) 0

(B)

(C)

(D)

6. An isolated charged point particle produces an electric field with magnitude at a point away. At a point from the particle the magnitude of the field is?

(A) (B) (C) (D)

General Instructions: • Closed Book, Open Minds! Please attempt all questions and work neatly. • Please SHADE your response to the MCQs on the ANSWER SHEET PROVIDED • Mark scheme [ Correct (1 mark); Incorrect (0 mark); No Response (−1 mark) ]

E

N ⋅C 2

C ⋅N −1

N ⋅C−1

C ⋅m−2

E

J ⋅C−1 ⋅m−1

J ⋅C−1

J ⋅CJ ⋅m−1

kqr

− kqr

kqr2

kq2

r2

5C 2m

5kQ25kQ425kQ2

25kQ4

d < r

kqr − d( )2

kqd 2

kqr2

E 2m4m

2.0E4.0E0.5E0.25E

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7. An eastbound electron, moving at a constant velocity, enters a region containing only a uniform electric field that is directed southwards as shown in the diagram below.

The electron will:

(A) disintegrate (B) reverse direction (C) accelerate (D) veer downwards

8. A proton traveling at a constant speed horizontally enters a region where the electric field is uniform and points south.

The general motion of the proton will be: (A) parabolic (B) circular (C) unchanged (D) completely reversed

9. A charged oil drop with a mass of is held suspended by a downward electric field of 300 N/C. The charge on the drop is:

(A) (B)

(C) (D)

10. The electric field at a distance of from an isolated point particle with a charge of is: (A)

(B) (C) (D)

11. Two small charged objects attract each other with a force F when separated by a distance . If the charge on each object is reduced to one-fourth of its original value and the distance between them is reduced to the force becomes:

(A)

(B)

(C)

(D)

12. The units of are:

(A) (B) (C) (D)

13. Two particles, one with charge +8 × 10−9 C and the other with charge −2 × 10−9 C, are apart.

What is the value of the electric field intensity, , midway between the 2 particles?

(A) 13.5 N/C (B) 135 N/C (C) 22.5 N/C (D) 225 N/C

14. Positive charge Q is uniformly distributed on a semicircular rod. What is the direction of the electric field at point P, the center of the semicircle?

(A) ↑ (B) ↘︎ (C) ← (D) →

15. The magnitude of the force of a 400-N/C electric field on a 0.02-C point charge is:

(A) (B) (C) (D)

electron

Electric Field, !E

−

2 ×10−4 kg

+1.5 µC−1.5 µC+6.5 µC−6.5 µC

0.1m2 ×10−9C

1.8 N /C180 N /C18 N /C1800 N /C

d

d / 2F16F8F4F2

14πε0

N 2 ⋅C 2

N ⋅m2 ⋅C−2

N ⋅m ⋅CN ⋅m2 ⋅C 2

4m

4 m

q1 q2−+

E = ?

E

8.0 N8.0 ×10−5 N8.0 ×10−3 N0.8 N

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25. Positive charge Q is uniformly distributed on a semicircular rod. What is the direction of theelectric field at point P, the center of the semicircle?

....................................................................................................................................................................................................................................

..........................................................................................................................................................................................................................................................

.......

.

........

•PQ

A.B.C.D.E.

ans: D

26. Positive charge +Q is uniformly distributed on the upper half a semicircular rod and negativecharge −Q is uniformly distributed on the lower half. What is the direction of the electric fieldat point P, the center of the semicircle?

....................................................................................................................................................................................................................................

..........................................................................................................................................................................................................................................................

......

..

........

........ •P

+Q

−Q

A.B.C.D.E.

ans: B

27. Positive charge +Q is uniformly distributed on the upper half a rod and negative charge −Qis uniformly distributed on the lower half. What is the direction of the electric field at pointP, on the perpendicular bisector of the rod?

•P+Q

−Q

A.B.C.D.E.

ans: B

338 Chapter 22: ELECTRIC FIELDS

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16. Consider the incomplete definition:

“The ___________________ at a point in an electric field is the __________________ in moving an infinitely small positive unit test charge from infinity to that point.”

The missing phrases are, respectively:

(A) potential energy, power gained (B) voltage, energy lost (C) electric force, power required (D) potential, work done

17. Let k denote coulomb’s constant. The potential energy of an isolated system containing only 1 electron and 1 proton separated by a distance of

is:

(A)

(B)

(C)

(D)

18. If 500J of work are required to carry a charged particle between two points with a potential difference of 20V, the magnitude of the charge on the particle is:

(A) (B) (C) (D) Cannot be computed without the path

19. An electron has charge and mass me. A proton has charge and mass 1840me. A “proton volt” has the energy equivalence:

(A)

(B)

(C)

(D)

20. An electron is accelerated from rest through a potential difference V. (Using the principle of energy conservation,) its final speed is proportional to:

(A) (B)

(C)

(D)

21. A 5-cm radius conducting sphere has a surface charge density of 2 × 10−6 C/m2 on its surface. Its electric potential, relative to the potential far away (i.e., at ‘infinity’), is:

(A) (B) (C) (D) (The surface area of a sphere is )

22. Eight identical spherical raindrops are each at a potential V, relative to the potential far away. They coalesce (stick) to make a single spherical raindrop whose potential is:

(A)

(B)

(C)

(D)

23. A farad is the same as a: (A) (B) (C) (D)

24. A unit of capacitance might be: (A) (B) (C) (D)

25. To charge a 1-F capacitor with 2 C requires a potential difference of:

(A) 2.0 V (B) 0.2 V (C) 5.0 V (D) 0.5 V

1µm

− ke2

1×10−6 J

ke2

1×10−6 J

− ke2

1×10−12 J

ke2

1×10−12 J

0.004 C12.5 C25 C

e−e

1 eV1

1840 eV

1840 eV1

1840 eV

VV 2

1VV

1.1×104V2.2 ×104V2.3×105V3.6 ×105V

4πr 2

V2V88VV4

CV −1

VC−1

JC−1

VA−1

JC−1

J 2C−1

CJ −1

C 2J −1

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26. Each plate of a capacitor stores a charge of magnitude 1 mC when a 100-V potential difference is applied. Its capacitance is

(A) (B)

(C) (D)

27. A parallel place capacitor has a 120-V potential difference applied across its plates that are apart. What is the magnitude of E-Field between the plates?

(A) (B) (C) (D) Not enough information provided

28. A capacitor C “has a charge Q”. The actual charges on its plates are:

(A)

(B) (C) (D)

29. A circuit containing a resistor in series with 2 capacitors connected in parallel is shown below.

The time constant of this circuit is:

(A)

(B)

(C)

(D)

30. The time constant RC has units of (A) second/farad (B) second/ohm (C) second/watt (D) seconds

31. A capacitor has an initial voltage of across its plates. It is connected in a simple RC series circuit to a dc supply. The governing equation for the capacitor voltage as a function of time is

(A)

(B)

(C)

(D)

32. A charged capacitor, , that was charged to a p.d., , is being discharged through a resistor,

. What quantity of charge, , remains on the capacitor after seconds?

(A)

(B)

(C)

(D)

33. A charged capacitor is being discharged through a resistor. At the end of 2 time constants, the charge remaining as a fraction of its initial value is:

(A) 0.13 (B) 0.86 (C) 0.14 (D) 0.87

34. A capacitor, in series with a resistor, is being charged. After 10 ms, its charge is half the final value. An approximation of the time constant is?

(A) (B) (C) (D)

35. Which of the following is best suited as the dielectric material in the design of a capacitor with a relatively large capacitance?

(A) air (B) paper (C) mica (D) zinc

5 µF10 µF50 µF100 µF

1mm

120 Vm−1

120 kVm−1

1.20×10−3 Vm−1

+Q, 0+Q / 2, −Q / 2+Q, −Q±Q, 0

τ = R(C1C2 )

τ = RC1C2C1 +C2

⎛

⎝⎜⎞

⎠⎟

τ = 12RC1 + RC2( )

τ = R(C1 +C2 )

4.5V

8.0V

vC (t) = 8.0e− tτ

vC (t) = 8.0 1− e− tτ

⎛

⎝⎜⎞

⎠⎟

vC (t) = 4.5+8.0e− tτ

vC (t) = 4.5+8.0 1− e− tτ

⎛

⎝⎜⎞

⎠⎟

CV0

R qC (t)t

CV0e− tτ

CV0 1− e− tτ

⎛

⎝⎜⎞

⎠⎟

CV0e− tτ

CV0

1− e− tτ

⎛

⎝⎜⎞

⎠⎟

14 ms10 ms2.9 ms6.3 ms

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36. The capacitance of a parallel-plate capacitor with plate area A and plate separation d is:

(A)

(B)

(C)

(D)

37. The capacitance of a parallel-plate capacitor can be increased by

(A) increasing the charge (B) decreasing the charge (C) increasing the plate separation (D) decreasing the plate separation

38. In a parallel plate capacitor, if the plate area is doubled and the plate separation is halved, then the capacitance is:

(A) doubled (B) halved (C) quadrupled (D) unchanged

39. In a series network of 4 capacitors, given that , , and

, across which of these devices is the p.d. the highest?

(A)

(B)

(C)

(D)

40. In a parallel network of 4 capacitors, given that , , and

, across which of these devices is the charge on a positive plate the lowest?

(A)

(B)

(C)

(D)

41. In a series network of 3 capacitors, given that , and , its

equivalent capacitance, , is

(A) (B)

(C) (D)

42. In a parallel network of 3 capacitors, given that , and , its

respective equivalent capacitance, , and total

energy stored when the total p.d. is is: (A) , (B) ,

(C) , (D) ,

43. The maximum displacement current through a capacitor occurs when its p.d., is

(A)

(B)

(C)

(D)

44. Which of the following is the correct relationship between relative permittivity, , absolute

permittivity of ‘free space’, and Coulomb’s constant, ?

(A)

(B)

(C)

(D)

45. Which of the following is NOT an example of an application that uses a capacitor?

(A) Television volume control (B) AC to smooth DC conversion (C) Radio station tuning (D) Emergency light flasher

- ENFIN -

ε0dAε0Add

4πε0Adε0A

C1 = 10µF C2 = 22µF C3 = 33µFC4 = 47µF

C1C2C3C4

C1 = 10µF C2 = 22µF C3 = 33µFC4 = 47µF

C1C2C3C4

C1 = 10µF C2 = 100µF C3 = 1000µFCS

1100µF110µF9.0µF0.111µF

C1 = 10µF C2 = 90µF C3 = 1000µFCP10 2V

1100µF 110mJ110µF 11mJ9.0µF 0.9mJ0.111µF 11.1µJ

VC (t)

VC (0+ ) =VS

VC (0+ ) = 0V

VC (∞) =VSVC (∞) = 0V

ε rε0

ke

πε rεokc =14

πε rεokc4

= 1

ε rεokc =π4

ε rεokc4

= π

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