Self-Check

'1 Define electric fleld strength.

2 Define potential ai a point.

3 State the relationship between field slrength of the field at a point, and the potential gradientat that point.

Application Questions

A lnteraction between Point Charges

1 Point charges, each of magnitude Q, are placed at three corners of a square as shown in thediaqram. The side of the square is L.

L-O' lnO (a) Draw 3 arrows at the fourth corner of the square toindicate the directions and relative magnitudes ofthe electric fields due to each charge.

L

(a) Determine the magnitude and direction of the resultant field.

t@) 0 239 tfrom -Q towards the for n 324

ttE.t lnh corner) (b) TIe"Lt

I

2 \a) Two ions A and B are separated by a dislance ol 0.72 nm in a vacuum. A has acharqe of +3.2 x 10 I' C and B has a charqe of -1.6 x 10 '' C.

(i) Calculate the force A exerts on B. I 8.9 x 10r0 Nl

(b) Determine the electric potential at the fourth comer due to the 3 charges-

(i') Calculate the torce B exerts on A.

(b) Without making detailed calculations, draw labeled arrows on the Fig. below torepresent

(i) the field E4 atthe point Xdue to the charge atAonly.(ii) the field Es at the Xdue to the charge at B only.(iii) the resultant field at X d ue to both charges.

(c) Sketch on the diagram, line representing the electric field caused by the two ions in

the region within the rectangle. lnclude the field line passing through X

X

BA

Two equal negative charges of each of -3.2 pC are situated at points X and Y, whichrepresents a diameter of a circle as shown. O is centre of the circle. AB is a diameter

perpendicular to XY. The diameter of the circle is 3.0 cm.

(a) A proton is placed at A then moved to O andfinally to B. Determine the direction and magnitudeof the force the proton experiences when it is at A,O and B.

I(a) 1.45 x10irN, o, 1.45 * 10i1 Nl(b) lf a stationary proton is released at A, describe the motion of the proton.

A

,,1- Z.Z p)j ,. ,-- S.Z 1,eO-------'-- P ax'1. oi

..i Y

i'.-.i-.B

Two point charges are positioned so that they are separaied by a distance of 2.0 cm asshown in the figure below. X is a point lying 5.0 cm away from the positive point charge. Themagnitude ofthe positive charge js 10.0 pC and the magnitude ofthe negative charge is 30.0pc.

5.0 cm 2Ocrn

(i) Calculate the magnitude and state the direction of the electric field strength at point X.

(ii) ln the figure above, sketch the electric field pattern around the h^/o charges.

(i;i) Determine the position where no net electric force will act on a test charge placed

there.

(iv) "There is no net electric force acting on a test charge in a region where the electricpotential is unifo.m." Explain whether this statement is valid.

B

5

Uniform Electric Field

Two large horizontal parallel conducting metal plates are situated 40 mm apartshown in the diagram. The potential of one plate is +20 V and the other is -30 V.

+ 20v

'v- 30v

The space behreen the plates is divided equally by 3 dotted lines. X and Y are two pointsthat lie on the lines as shown above. The field within the plate is assumed uniform.

(a) Draw an arrow in the space between ihe 2 plates to show direction of the electtic fieldwithin the plate.

(b) What is the potential diiference between X and Y?

(c) What is the amount of work needed to bring a proton from Y to X?

(d) A siationary electron is released, within the field, at the surface of the -30 V plateDescribe its subsequent motion.

(e) Determine the acceleration of the electron.

(f) How long does iL take to reach the +20 V plale?

I(b)25V (c)4.0x10-13J (e) 1.20' 101'?ms'? (f)2.58*10'sl

A beam of electrons enters a uniform electric field between h,vo places of length, /, 50 cm,separated by a distance, d, 20 cm, as shown in Figure 6. One plate is at a potential of +30 Vwhile the other is at a potential of -30 V.Find the angular deflection of the electron beam. The velocity of the electron beam as itenLerc the electric field, u, is 2.65 x 106 m s I. 175"1(Charge on electron is L6 " 1O-1e C and mass is 9.11 '( 1Or1 kg)

20 cm

Fig.6

-30 v

50 cm

What is meant by uniform electric field?

The diagram below shows ihree points X, Y and Z forming equilateral triangle of side s in auniform electric field of strength E. A unit neoative charge is moved from X to Y, from Y to Zand from Z back to X.

E

Determine the work done, in each case, in moving the charge along the various paths?(a) XtoY

(b) YloZ

(c) Zto X

What will the answers be to (a), (b) and (c) if the charge were positive?

[ (a) 0.866 Es (b) 0.866 Es (c)0]

The diaqram shows a uniform field in which the lines of equal potential are spaced 2.0 cmapart.

50v

electric field

0V -50V -100V'1 00 v

i2.0cm 2.0cm i2.0cm i2.0cm i

<---_- '<

>< _---'>ia----------+ lines ofequipotential(a) Determine the field strength of this electric field.

(b) A proton is placed in the field at the point X.(i) Deiermine the magnitude and direction of the force it experiences.

(ii) Calculate its electrical potential energy at point X.

(iii) lf the proton is moved to point Y, determine its electrical potential energyat point Y.

(iv) What is the chanqe in the

'1. electrical potential, and

2. electrical potential energy?

(c) Repeat (b), but change the charge to an electron instead of the proton.

[ (a) 25OO Vm-1(iv) 1. 100 V

(iii) B.O x 10 13 J(bxi) 4.0 x 1o16N (ii)8.0x 10 18J

(iv) 2. 1.6 x 1O-1?J l

c

IComparison between Electrical and Gravitational Fields

(a) (i) What is the analogous expression for a gravitational field?

(ii) Wite down the units of electric fleld strength and potential and ofgravitational field strength and potential.

(b) ABC is a triangle in which CA = CB = r. IntheFig.'11.1 below, charges -Q and+Q are placed at A and B respectively and, in Fig. '11.2, equal point masses mare situated at A and B.

L, '.R

r\ rr'rFig. '11.1

B

mmFis. 11.2

(i) !n Fig. 1, in which direction relative to the x- and y-directions does theresultant electric field at c act.

(ii) ln Fig. 2, in which direction relative to the x- and y-directions does theresultant gravitational field at C act?

(iii) Determine the electric and gravitational potential at C.

2GmI(iii) 0,

-l

Structured Question

10(a) The Millikan experiment is said to provide experimental evidence for lhe quantization of

charge. What is meantby quantization2

(b) The arrangement in the flgure below shows an oil droplet between tvvo metal plates.

.nUrldroplet \J Melal plates

/

When no p.d. is applied across the plates, the oil drop is observed to fall at a terminalvelocity v. Assume upthrust is negligible.

(i) Draw a clearly labeled free-body diagram to show the forces acting on ihe oil drop.

(ii) Using the following information, determine the radius r of the oil drop.

Terminal velocity of oildrop, v= 2.5 r '10 ! m s 1

Separation of plates, d = 20 mmViscosity of air, I = 1.8 x 10-sNsm'?Density of oil, p" = 9OO kg m-3

Stoke's law (sphere), f = 6rrlv

(c) (i) Another oil drop of radius 1.90 Fm carries 8 electrons, and remains stationarybetween the plates. Determine the p.d. applied across the plates, with the upper plate

being positive. [You may use the information given in (bXii) where necessary]

(ii) lt this oil loses an electron, calculate the initial acceleration ol the drop.

*** End of Tutorial ***