The work done on a beta-minus particle wh(xxd,1etlc+z noqz7:f:)m z sen moving it from Y to X is found to be −10eV. Equipotential lines are represented by the dashed lines in the diagramnz+e m xl( z)cq1sx:,do :z7tf.
What is the work done by the field on an electron when it is moved from Z to W in the field shown?

  A point charge is moved between9al8+wypf k3 x two parallel plates separated by a distance of 5cm. The potential difference betwex+fy9 lk a3w8pen the points is 50V.
What is the average electric field E?

  Which of the following correctly lists the fundamental forces q 6 2( 0xgn:r5psjegoyin decreasing order ofe q6s p ygng5x0(jor2: strength?

  A beam of electrons enters a uniform electric fieypglkqn1j(kv 3p(3l4 ld, as shown.



What effect does this field have on the horizontal and vertical components of the electrons' velocity?

  A hydrogen nucleus is held stationary in a unvt1;:q7izn x)k:* hb ws/rfl4gqzf j4iform vertical electric field, represented by the arnkq7 z:btgjxiq) f4 *:s rfwzvl4/h;1 rows. Which of the paths shown would require the largest work to be done on the hydrogen nucleus?

  Two charges, separated by a large distance, are shown belowb671 yo;ukhis8nfz2 deg1im:, along with the electrico1ki b17g ;z 68msefyuhni d:2 field lines around each charge.

Which of the following statements is correct?
I. The charge q is positive.
II. The charge q is equal in magnitude to +Q.
III. The electric field magnitude near the charge q is greater than the magnitude of the field near the charge +Q.

  A positive and a negative charge of 7kk l/2, psiadb1l xb9d *ye4pequal magnitude are located on the same horizontal li p9/p kal 7dk2d,y blbx*se41ine.

What is the direction of the net electric field at the point marked X, equidistant from the two charges?

  A plastic rod carrying abj yf()od ),94xx mfuh uniformly distributed positive charge is bent into a quarter-circle. What is thef xx4h)uo y,)9j(fmbd direction of the electric field at point P?

  A non-conducting sphere with radius R kb8e be6 p5-qhh7bfp: carries a uniformly distributed positive charge with6h qe 8:5bkbepp7b -fh charge per unit volume ρ.Point P is at a distance r from the center of the sphere.


The electric field outside this sphere is given by $E_{out}$ = $\frac{ρR^3}{​3ϵ_0​r^2}$
While the electric field inside the sphere is given by $E_{in}$ = $\frac{ρr}{​3ϵ_0​}$
Where $ϵ_0$​ is the free space permittivity.
The radius of the sphere is 2.0 cm.
1.Calculate ρ when the charge on the sphere is 0.1 μC. ρ =    $\times10^−3\,Cm^{−3}$
2.Determine the electric field at point P, when =r=3cm. E =    $\times10^5\,NC^{−1}$
3.In the space provided, sketch the variation of electric field E with the distance from the center of the sphere r.


A positive charge is released from the surface of the sphere.
4.Describe the motion of this released charge.

  The diagram shows the equipotential lines in a fie4xxo e 4unfwc905(lc6mi kyw-ld due to A and B. What may be r c6(4y uxxlncfo9i 45e0wm-w kepresented by A and B?

I. 2 equal masses.
II. 2 equal charges of the same sign.
III. 2 equal charges of opposite sign

  An electron enters an elwol2zbh) qqv+u0 *f9sjatv00c r:l ( uectric field represented by the equipotential lines shown by the lines in the diagram. The electron’s path is shown by the d0 w:suqv) blo0*+h2qaj( r9flzt v0cuotted line.

What is the path of an alpha particle entering the same field with the same velocity as the electron?

  An atom is being modeled with an electron assumxov b6oyx-9mtu9.wf7 (;c ym wed to be orbiting the nucleus in the first energy level with a speew96mbcxy ymv t.xf w(- 9;o7oud of  $2.18\times10^6ms^{-1}$
The orbital radius of the ground state, in m, is given by
$r=(0.53\times10^{−10})n^2$
Where
$n$ = order of the energy level.
1.Determine the charge of the nucleus. q =    $\times10^{−19}$C
2.(1)The electron moves to the second energy level where it orbits with a kinetic energy of $5.44\times10^{−19}\,J$.
(2)Explain whether the centripetal acceleration increases, decreases or stays the same.
Calculate the orbital period of the electron in the second energy level. T =    $10^{−15}\,s$

Two positive charges 2Qr)4yjhectl 9yw;8b .o and Q are located as shown in the diagram. Some of the electric 8wo.9bey4)ty ;hlj rc field lines due to the charges are shown on the diagram. Points P and S are two points as located on the diagram.



1.Define the term electric potential.
2.Sketch the equipotential line that passes through point P.
3.A positive charge is moved from point P to point S. State and explain how the electric potential energy changes due to this move.

  Which of the following pairs of graphs represents how the electozsz:cz v x8z1.jx/0v .6oocv ric field and the electric potential due to a hollow conducting sphere vary with distance from the voz.vx:scz0.v81 6xco/ ojzz center? The origin of the graph represents the center of the sphere.

  Which of the following is equl7n58/k bey m5:kq3nvex 4v soivalent to the unit of electric potential difference? k3sq8:7/eb 4kyn5onx5evv ml

  Two point charges of −4.0μC a1k)h7cuiop qg zl /,oz (c4au7nd 88.0μC are separated by a distance r=2.0cm as shown in the d/z4ouc,)kp(uh 7gz i7oc1qlaiagram

1.State what is meant by electric field strength.
2.Calculate the magnitude of the electrostatic force exerted on each charge. F =    N
3.Three points A, B and C are at the regions shown in the diagram.

(1)Deduce which point(s) could have zero electric field. Explain your reasoning.
(2)Calculate the distance(s) from charge q1​ to the point(s) of zero electric field. X =    cm
(3)The two charges are inserted in a water tank separated by the same distance as in air.The permittivity of water is 80 times that of free space.

Discuss what change, if any, will occur in the location of the point(s) of zero electric field in this case. Justify your answer.
4.The charges are removed from the water tank, and $q_1​$ is replaced by another charge that is identical to $q_2$​.
Point P is at equidistance d from both charges as shown.

Draw an arrow indicating the direction of the electric field at point P.

1.Define electric potential energyaeiy7b k;7kqmtz a34- .
2.Two parallel plates are at potentials −2V and +12V as shown in the diagram.

On the diagram, sketch
（1）The pattern of electric field lines between the two plates
（2）The equipotential line which represents zero volts.
3.Calculate the work done by the electric field on a charge of −6.0μC when it is moved from plate B to plate A.

  A positive charge Q and four points pxgu t4),nsbs6l h5g, on equipotential lines are represented in the diagr ,stbxus, lpgg hn645)am shown.
A negative ion is moved from location 1 to 2, then to 3 and finally to 4. Which of the following gives the correct nature of the net work done on the ion during each section of this movement?

  The diagram shows the equipotential surfaces of two chargkcq::/hd1w:al*j k dyn3+fil es.

Which of the following can be the directions of the electric field at points A and B?

  A charge of X and a charge of 20nC are he5krg*kr h zy.h)9 9x*coayr p*ld at a fixed distance.

A point where the electric field is zero can only be found in region 1. Which of the following statements is true about the charge on X

  Two charges separated by a distance r are placed in a medium with permrv)m i96da-j27 gpsm4ggfgt+ ittivity ϵ. The charges are then moved to air so that they have the same force between them as g-pr+2dm4igtg6s9jg 7f v )am that in the medium.
What is the distance between the charges in air, knowing that $ϵ$=$ϵ_r$​$ϵ_0$​?

  An electron is released from the negative plate of two oppositely charged p w+(qd c1yjc7harallel plates placed a fixed distance apart. The potential difference between the two plates is V, and ccy1wd +7j hq(the electron reaches the positive plate with a speed v.
What would be the final speed of the electron if the distance between the plates remained the same, but the potential difference between them were doubled?

  A proton and another object with charge +e exert electrical anow; z-ow037xek*nb m( 5zhukq d gravitational forces on one another. To the nearest order of magnitude, what mass must the object have to be so that the net force acting on it is zero n*-obe53 u0(wz xw;7kzhm kqo?

  Equipotential lines representing*a+8tzdtv4u(- r zubq the corresponding potentials are shown in the diagram, in an electric fiel-tr( vtuz8q+ z*4bu add.
Which of the following is a correct statement regarding this electric field?

  Two positive charges ,nzd( jb *z0/gik m3/ /s4v elbtutvzj::lt9f$q_1$​ and $q_2$​ are separated by a distance d. A third positive charge q is placed at a distance $\frac{d}{4}$ from $q_1$​ so that the charge q is in equilibrium.


What is the ratio $\frac{q_1}{q_2}$

  Four fixed charged point particles are av:y7w-4lwt ee-fz it:t the vertices of a rectangle. Which arrow represents the net electric field at tfwz yw 7:4tlee-iv- :the center of the rectangle?

  Four identical negatively charged objects move in an electjv/xx / nxjip,(2 e5vyric field along paths shown as arrows below. Equipotential lines for the field are shown. Initiaey/xxvn,i/x5j( j v2p lly, all four objects have the same kinetic energy.

What is the relationship between the kinetic energies of the objects at the end of their paths?

  Two parallel plates are separated by 5-puz o4, c*pi kzel(fa distance d and connected to a battery of potential difference V as shown in the diagram. A proton released from the positive plate gains a speed v whp-lzfkoc 4e5( pi,z*uen it reaches the opposite plate.
The separation of the plates is decreased to $\frac{d}{2}$​.
What would be the speed gained by an alpha particle released from the positive plate, when it reaches the opposite plate?

  Two positive charges of magnitude 2C and 8C respectivel4x0dl irxm o8+ye 24vfvck,3cy are placed 9cm apart. A third charge is introduced betwf3,8lx0+rmev 4ci vycdk2x o4een the two charges as shown below;


At what separation, X, from the 2C charge is the electric field strength equal to zero?

  The diagram shows equipoth 0+.5nkm+ bqayja;jzential lines due to a point charge.
A second point charge of 0.8μC is moved from X to Y.
What is the work done on this charge?

  In the following diagr-t i-/8utmz .u5jm c 2n3ii7am-aiovaz0br 0pam, the size of the charges is small compared to the distancem2b-3-8r0uv n/tjcai z.ouiaamz07 t5imi p- R.



What is the direction of the force on the charge in the center?

  Estimate the speed of an alpha particle that has accelerated frjt 86vz .t;qchom rest in a unif.httz6cq v8j ;orm electric field E=50 $^{−1}$ over a distance of 2.0m.

  The graph shows the variation of the total electr fx2z 8ld3;3vaem,5;rxh ) koqvmqc. pic potential due to two point electrx3v;vfxro kqae ) z,5 qm2 lhcmp;d38.ic charges $q_1$​ and $q_2$ located 4.0m apart. The distance r is defined to be zero at the location of $q_1$.

What is the ratio of $\frac{q_1}{q_2}$

  The graph shows the variation of the electric potential due to tc;w w6lhcre7t7k2 h8a point charge as a 2rh7e ttl68cw;ch7 wkfunction the distance r from its center.

Which of the following gives the work done by the electric field‾by the electric field​ on a charge of −3μC when it is moved from $r_1$​ to $r_2$​ ?

  A conducting sphere has a radius of 20cm and a)gj0j, ,0arewzlmy7m:vs k h3 charge of +3.2μC. Point A is used to describe a location 20cm from the surface ofm 3sy,:)007wj garm jzhevlk, the sphere.

1.Calculate the electric potential at the surface of the sphere. State the correct SI unit for your answer. V=    $\times10^5\,v$
2.(1)On the axes given, sketch the variation of the electric potential due to the sphere with distance from its surface‾from its surface​. Label point A on the graph you have drawn.


(2)Without calculation, outline how the electric field strength at A may be determined using the graph you have drawn
(3)A proton is initially held stationary at the surface of the sphere. The proton is moved from the surface of the sphere to point A. Calculate the work done on the proton. W =    $\times10^{-14}\,J$
3.The proton is released from point A. Outline the subsequent motion of the proton.

  Two point charges are separated by a dista e cnaq o 2,e)ev9/rw.y+kxnh9nce r as shown.

The negative charge's acceleration is 3 times that of the positive charge.
What is the ratio $\frac{Gravitational force​}{Electrostatic force}$ between the two point charges?

  Four point charges are placed as shown on the corners of a square. Charges of 4m:6671bzd sx5smeag 4o,d j qxzkp6o+2Q and −Q, and unknown charges A andozz 4 mmdgs:e66x, xb5q4kjp 1 sa7do6 B are located as shown on the diagram.

At the center of the square, the total potential is zero, but the resultant electric field is not zero.
Which of the following is a possible combination for the charges A and B?