TUTORIAL 16: ELECTROSTATICS

16.1 Coulomb’s law

a) State Coulomb’s law, 22

o4 r

kQq

r

QqF

.

b) Sketch the force diagram and apply Coulomb’s law for a system of point charges.

16.2 Electric field

a) Define electric field.

b) Define and use electric field strength, oq

FE

.

c) Sketch the electric field lines of isolated point charge, two point charges and

uniformly charged parallel plates.

d) Sketch the electric field strength diagram and determine electric field strength, E

for a system of charges.

16.3 Charge in a uniform electric field

a) Explain quantitatively with the aid of a diagram the motion of a charge in a

uniform electric field.

16.4 Electric Potential

a) Define electric potential.

b) Define and sketch equipotential lines and surfaces of

i) an isolated charge

ii) a uniform electric field

c) Use r

kQV for a point charge and a system of charges.

d) Calculate potential difference between two points,

VAB = VA – VB

o

BAAB

q

WV

e) Use d

VE for uniform electric field.

f) Deduce the change in potential energy, U between two points in an electric field,

VqU

g) Calculate potential energy of a system of point charges,

23

32

13

31

12

21

r

qq

r

qq

r

qqkU

TUTORIAL 16

(ELECTROSTATIC)

SECTION A

1. Which of the following statement is not correct?

A There are two types of charges differing in signs

B The charges are conserved and they have discrete values

C The smallest value of a charge is that of an electron or a proton

D Electric charges can be created by rubbing or friction

2. Which diagram best represents the electric field around a negatively charged

particle?

A B C D

3. At a distance R away from a point charge, the electric field has a strength of E and

the electric potential is V. At a point R/2 away from the same point charge which

of the following is true?

Electric field strength Electric potential

A 4E 4V

B 2E 2V

C 2E 4V

D 4E 2V

4. A proton accelerates from rest in a uniform electric field of 640 N/C . At some

later time, its speed is 1.20x106

m s-1

.Calculate the acceleration of the proton.

A. 61.32 Gm s-2

B. 31.30 Gm s-2

C. 20.42 Gm s-2

D. 22.67 Gm s-2

5. Which of the following statements is true about electrically equipotential surfaces?

A The charge density is uniform.

B The electric field at any point on the equipotential surface is zero

C There is no electric potential difference between 2 nearby electrically

equipotential surfaces.

D no work is done to move a charge along an equipotential surface.

SECTION B

6. (a) State Coulomb’s Law

20 cm 15 cm

q2 q1 q3

FIGURE 1

(b) Three point charges, q1 = +3.0 μC, q2 = -4.0 μC and q3 = – 7.0 μC are

placed 20 cm and 15 cm apart on a straight line in air as shown in

FIGURE 1. What is the magnitude and direction of the nett electrostatic

force acting on charge q1

( Ans: 5.7 N to the right)

7. Two equal positive point charges q1 = q2 = 2.0 μC are located at x = 0, y = 0.3

m and x = 0, y = - 0.30 m respectively. What are the magnitude and direction

of the total electric force that these charges exert on a third point charge Q =

4.0 μC at x = 0.40 m, y = 0?

(Ans: 0.46 N to the right)

8. When a test charge q = 2nC is placed at the origin, it experiences a force of

8.0 10-4

N. Calculate the magnitude of electric field at the origin.

(Ans; 5100.4 NC-1

)

9. Sketch an electric field lines pattern for following cases :

i) Two equal positive charges, +2Q and +2Q

ii) Negative point charge

iii) Uniformly charged parallel plates

10.

A beam of electrons enters the uniform electric field between two parallel plates

as shown in FIGURE 2.

(a) Sketch the path of the electron beam in the electric field, and after emerging

from the electric field.

(b) Explain the shape of the path

11.

Two parallel plates are set a distance of 15 mm apart in a vacuum as illustrated in

FIGURE 3. The top plate is at potential of +200 V and the bottom plate is at

potential -200 V.

(a) Copy FIGURE 3 and draw lines to show the electric field between the plates

and show a possible path of the electron as it passes between the plates.

(b) Determine the magnitude of the acceleration of the electron .

(Ans: 151027.4 N)

+200 V

-200 V

e 15 mm

e

FIGURE 2

FIGURE 3

12.

FIGURE 4 shows a section of the deflection system of a cathode ray oscilloscope.

An electron travelling at a speed of 1.5 x 107

m s-1

enter the space between two

parallel metal plates 60 mm long. The electric field between the plates is 4.0x103

V m-1

.

(a) Copy the figure and sketch the path of the electron in between plates, and

after emerging from the space between the plates.

(b) Calculate the vertical component of velocity as it leaves the region between

the plates. (Ans; 61081.2 m s-1

)

13. (a) Sketch equipotential lines and surfaces of

(i) a positive charge

(ii) a uniform electric field

(b) Two point charges of 4 µC and 16 µC are separated by a distance of 10

mm. A point P is at a distance of 8 mm from the 4 µC charge and 6 mm

from the 16 µC charge.

(i) Calculate the electric potential at P.

(ii) What is the electric potential energy of a charge of 10 µC at P?

(Ans: 71085.2 V, 285 J)

14. (a) Explain

(i) why electric field strength is a vector quantity which has

magnitude and direction.

(ii) electric potential is a scalar which has only magnitude.

(b) Two parallel metal plates separated by a distance of 1.5 mm are charged

until the potential difference between the plates is 6 V. What is the electric

field intensity between the plates?

(Ans: 3104 V m-1

)

0 V

+80 V

1.5x107

m

s-1

20 mm

60 mm

FIGURE 4

15. (a) What is the work required to transfer a charge of 6 µC against a potential

difference of 110 V?

(Ans: 4106.6 J)

(b)

Three point charges of +q, +2q and -3q are arranged as shown in FIGURE 5.

Calculate the electric potential energy of the system of three charges.

(Ans: a

kq2

59.7 J)

FIGURE 5

+q

-3q +2q

a

a