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Old-Exam. Questions-Ch. 24-082 (Dr. Naqvi-Phys102-04-06)
T081: Q10.: Points A (2.0 m, 3.0 m) and B (5.0 m, 7.0 m) are located in a region where the electric field is uniform and
is given by E  4.0 iˆ  3.0 jˆ N/C . What is potential difference (VA-VB)? (Ans: 24 V)


Q#11: Eight isolated identical spherical raindrops are each at a potential of 100 V at the surface, relative to the potential at
infinity. They are combined together to make one spherical raindrop whose potential at the surface is: (Ans: 400 V)
Q12. Point charges q and Q are placed as shown in Fig. 4. If q = +2.0 nC and Q = -2.0 nC, a = 3.0 m, and b = 4.0 m, what
is the electric potential difference (V A-VB)? (Ans: 4.8 V)
Q13.Two identical and isolated 8.0 C point charges are positioned on the x-axis, one is at x = +1.0 m and the other is at x
= -1.0 m. They are released from rest simultaneously. What is the kinetic energy of either of the charges after it has moved
2.0 m along the x axis? (Ans: 96 mJ)
Q14.: A conducting sphere 1 with radius R has a positive charge Q. Another conducting sphere 2 with radius 2 R is far
from sphere 1 and initially uncharged. After the separated spheres are connected with a thin conducting wire the two
spheres end up with charges q1 and q2. Which of the following statements is correct? (Ans: both spheres are at same)
potential.
Fig. 1, T081
Fig. 1, T072
Fig. 2, T072
T072
Q#9: In the figure 1 , two particles with charges Q and −Q are fixed at the vertices of an equilateral triangle with sides of
length a. The work required to move a particle with charge q from point i to point f is: (Ans: 0)
Q10.: Over a certain region of space, the electric potential is give by: V(x,y) = x2+y2+2xy where V is in volts and x and y
are in meters. Find the magnitude of the electric field at the point P (1.0 , 2.0). (Ans: 8.5 N/C)
Q11. In the figure 2 , two conducting spheres, one having twice the diameter of the other, are separated by a distance large
compared to their diameters. Initially, the smaller sphere (1) has charge q and the larger sphere (2) is uncharged. If the
spheres are then connected by a long thin conducting wire: (Ans: 1 and 2 have the same potential)
Q12. A charge q1 = -5.0 μC and a charge q2 = 6.0μC are located at (8.0 cm, 0.0) and (0.0 cm, 6.0 cm) respectively in the
xy plane. How much work was done, by an external agent, to bring these charges to their final positions starting from
infinite separation.[Consider V = 0 at infinity] (Ans: – 2.7 J)
Q#13: A particle, with mass = 9.0×10-9 kg and charge = +8 nC , has a kinetic energy of 36 μJ at point A and moves to
point B where the potential is 3.0×10 3 V greater than that at point A. What is the particle's kinetic energy at point B? (Ans:
12 μJ)
T071: Q10. What is the external work required to bring four 3.0×10-9 C positive point charges from infinity and place
them at the corner of a square of side 0.12 m (Ans: +3.7 μJ)
Q11. A point charge q1 = + 2.4 μC is held stationary at the origin. A second point charge q2 = - 4.3 μC moves from x1=
0.15 m, y1= 0 to a point x2 = 0.25 m, y2 = 0.25 m. How much is work done by the electric force on q2 ? (Ans: 0.36 J)
Q12. An electron is accelerated from a speed of 3×106 m/s to 8×106 m/s. Calculate the potential through which electron
has to pass to gain this acceleration? (Ans: 157 V)
Q13. The electric potential in a certain region is described by V(x,y, z) = 2xy- 4x2 + 6 y. Find the magnitude of the net
electric field at x = -1 and y = 1? (Ans: 11 N/C)
Q14. A conducting sphere with a radius of 10 cm, has a surface charge density of 4 ×10 −6 C/m2. The electric potential, at r
= 5 cm from the center of the sphere is ( assume V= 0 at infinity): (Ans: 4.5×104 V)
T062: Q8. Calculate the ratio of the speed of a proton to that of an electron, both accelerated through the same potential
difference. (Ans: 0.023)
Q10.: Two charged spherical conductors having radii 4.0 cm and 6.0 cm are connected by a long conducting wire. A total
charge of 20 μC is placed on this combination of two spheres. Find the charges on each sphere (smaller first). (8 μC and 12
μC)
Q11.: Figure (3) shows three charges located at the corners of a triangle. How much energy would be needed to remove the
4 μC charge to infinity? [Assume V = 0 at infinity.] (8.2J)
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Q12: Three concentric spherical shells A, B and C, of radii a, b and c (a<b<c), have charges q, -q and q respectively. The
potential of C is: Vc=kq/c:
T061:
−6
2
Q#10. A 5-cm radius conducting sphere has a surface charge density of 2 ×10 C/m on its surface. The electric potential, at r =
4
2.5 cm from the center of the sphere is: [Assume V = 0 at infinity.] (Ans:1.1 × 10 V )
Q#11. The diagram in Fig. 1 shows four pairs of, identical, large parallel conducting plates. The value of the electric potential is
given for each plate. Rank the pairs according to the magnitude of the electric field between the plates, least to greatest.
( Ans: 2,4, 1, 3)
Q#12. An electron starts from rest at a point 10 cm from a positively charged conducting plate, with a surface charge density σ
-9
2
= +1 × 10 C/m . The electron is attracted to the plate until it collides with the plate. With what speed will the electron collide
6
with plate? (Ans: 2.0 × 10 m/s
-9
Q#13. A point charge of 5.0 × 10 C is transferred, by an external agent, from infinity to the surface of a ball of radius 5.0 cm.
-4
2
If the ball has the charge density 5.0 × 10 C/m , then the amount of work done, by the external agent, in the process is:
-2
[Assume V = 0 at infinity.] (Ans: 1.4×10 J )
Fig. 1, T061
T052: Q#2. A particle with a charge of 5.5 x 10
Fig. 3, T062
Fig. 6, T052
-8
C is fixed at the origin. How much work is done by external agent to move
-8
-5
a charge of –2.3 x 10 C from point A to point B shown in figure 6. (Ans: 6.0 x 10 J )
Q#11. Two conducting spheres, one having twice the diameter of the other, are separated by a distance large compared to their
diameters. The smaller sphere has charge q and the larger sphere is uncharged. If the spheres are connected by a long thin
conducting wire: (Ans: 1 and 2 have the same potential )
Q#13. Two electrons are initially far away. Each electron is moving toward the other one with a speed of 500 m/s. Find the
closest distance they can get to each other. (Ans: 1.01 mm)
Q#16. In a certain region of the xy plane, the electric potential is given by V (x,y) = 2xy – 3x2 + 5y, where At which point is the
electric field equal to zero? (Ans: –2.5, –7.5)
Q#18. A charged solid conducting sphere has a radius = 20 cm and a potential of 400V. Calculate the electric field 40 cm from
the center of the sphere, (Ans: 500 V/m)
T051: Q#10. A proton moves in a uniform electric field of 2.5×10 7 N/C from point A to point B by traveling a distance of
1.5 m. Find the work done and the potential difference between point a and b.(Ans: 6×10 -12 J; 3.75 ×10 7 V.)
Q#11. The electric potential at point in an XY plane is given by V = 3X 2 – 4Y 2 .what are the magnitude and direction of the
electric field at a point (4m, 2m) ? (Ans: E = 29 N/C and 146 counterclockwise from + x-axix.)
Q#12. What is the net potential at point P due to four point charges arranged in th configuration as shown in the Figure 1. Here
q = 36 nC, d = 0.5 m. )( Ans: Vp = 324 V.)
T042:Q11. Two oppositely charged parallel plates, 0.02 m apart, produce a uniform electric field between the plates. The
potential energy U(J) of an electron in the field varies with displacement x(m) from one of the plates as shown in figure 5. What
is the magnitude of the force on the electron? (A1 7.5*10**(-15) N.).
Q#12 A point charge Q, at the center of a circle, is surrounded by six charges each of magnitude q at a distance r as shown in
figure 4. How much work is done by an external agent to remove the charge Q from the center to infinity? [Consider the
electrostatic potential at infinity = 0 ] (Ans: zero.)
Q#13 Two protons, P, are fixed 6.0 m apart, as shown in figure 7. An electron, e, is released from point A. Find its speed at
point O, midway between the protons. (Ans: 11.6 m/s.)
Q#14 Figure 6 shows three points X, Y and Z forming an equilateral triangle of side S in a uniform electric field of strength E.
A unit positive test charge is moved from X to Y, then from Y to Z, and from Z back to X. Which one of the following
correctly gives the work done by an external agent in moving the charge along the various parts of the path? (Ans: 0, E*S*Sin(60 degrees) , + E*S*Sin(60 degrees).)
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Q#15 Over a certain region of space, the electric potential is give by: V(x,y) = x**2 +y**2 +2*x*y. Find the angle that the
electric field vector makes with Z-axis at the point P(1.0,2.0,0.0) (Ans: 90 degrees.)
Fig.1 , T051
Fig. 4, T042
Fig. 7, T042
 T041
Q#1: In figure 3, two large horizontal metal plates are separated by 4 mm. The lower plate is at a potential of 6.0 V. What potential should be applied to the upper plate to create an electric field of strength 4000 V/m UPWARDS in the
space between the plates? (Ans: -22 V.)
Q#2: In figure 4, the point charge Q1 causes an electric potential of 60 V and an electric field strength of 30 V/m at P, and the
the point charge Q2, separately, causes an electric potential of 120 V and electric field strength of 40 V/m at P. Which of the
following gives possible values of potential and field strength at P due to the joint action of Q1 and Q2? (Ans: 180 V, 50 V/m).
Q#3: In the xy plane, a charge q1 = 3.0 micro-C located at (3.0 cm, 0.0) and another charge q2 = -4.0 micro-C located at (0.0
cm, 4.0 cm). How much work must be done, by an external agent, to bring these charges to their fixed positions starting from
infinite separation. [Consider V = 0 at infinity] (Ans: -2.2 J)
Q#4: If an isolated metal sphere of radius r = 10 cm has a net charge of 4.0 micro-C. What is the potential on the surface of the
sphere? [Consider V = 0 at infinity] (Ans: 3.6*10**5 V.)
Q#5: It is required 1.0 mJ of work to move two identical positive charges +q from infinite separation so that they are separated
by a distance a. How much work is required to move four identical positive charges +q from infinite separation so that they are
arranged at the corner of a square with edge length a? [Consider V = 0 at infinity] (Ans: 5.4 mJ)
S
X
Y
Z
E
Figure 6
Fig. 6, T042
Fig. 4, T041
Fig. 3, T041
 T032:
Fi g. 9, T032
Q#1: Find the electrostatic potential at x = 0 for the following distribution of charges:-2q at x= 10 cm and -2q
at x= -10 cm. [Take q = 1.0*10**(-9) C, and the electrostatic potential at infinity = 0 (Ans: -360 V.)
Q#2: Three point charges are initially infinitely far apart. Two of the point charges are identical and have charge Q. If zero net
work is required to assemble the three charges at the corners of an equilateral triangle of side d, then the value of the third
charge is (Ans: - Q/2.)
Q#3: Consider two concentric conducting shells of radii (a) and (b), b > a. The smaller (inner) shell has a positive charge (q)
and the larger (outer) shell has a charge (Q). If the potential of the inner shell is zero, what is the value of Q? (Ans: Q = -b*q/a.)
Q#4: In figure 9, two equal positive charges, each of magnitude 5.0*10**(-5) C, are fixed at point A and B separated by a
distance of 6 m. An equal and opposite charge moves towards them along the line CO. At point C, 4.0 m from O, the kinetic
energy of the moving charge is 4.0 J. What is the kinetic energy of this charge when it passes point O? (Ans:10.0 J.)
243
Q#5: The potential of a charge distribution is given by: V(x,y) = A [y*(x**2)- x*(y**2)], where A is in appropriate units. The
electric field will be zero at the point: (Ans: x = 0, and y = 0.)
T031:Q#1:
The electric potential at points in the xy–plane is given by: V = (x**3 - 2*x*y) Volts, where x and y are in
meters. The magnitude of the electric field at the point with the coordinates x = 1 m and y = 2 m is: (Ans: Sqrt(5) V/m.)
Q#2: In figure (7), what is the net potential at point P due to the four point charges if V = 0 at infinity ? [take d = 2 cm,
q = 1.0 micro-C]. (Ans: 9.0*10**5 V.)
Q#3: Which one of the following statements is true? (Ans: The electric field lines are perpendicular to the equipotent
surfaces.)
Q#4: Two balls with charges 5.0 micro-C and 10 micro-C are at a distance of 1.0 m from each other. In order to
reduce the distance between them to 0.5 m the amount of work to be performed is: (Ans: 0.45 J.)
Fig. T031
Fig. 5, T012
Fig. 4, T012
Figure 6-T012
Figure 2-T002
T012:
Q#1: What is the external work required to bring four 2.0*10**(-9) C point charges from infinity and to
place them at the corner of a square of side 0.14 m (Ans: 1.4*10**(-6) Joule.)
Q#2: In figure (4), an electron moves from point 'I' to point 'F' in a uniform electric field directed as shown in the figure.
(Ans: The electric field does positive work on the electron.)
Q#3: In figure (5), a hollow sphere, of radius r that carries a negative charge -q, is put inside another hollow sphere, of radius
R that carries a positive charge Q. At a distance x from the common center, such that r < x < R, the electric
potential is: (Ans: k*[(Q/R)-(q/x)].)
Q#4: In figure (6), Q1 = 2.0*10**(-6) C and Q2 = - 2.0*10**(-6) C. What is the external work needed to move a charge Q =
- 4.0*10**(-6) C at constant speed from point A at the center of the square to point B at the corner?
(Ans: Zero.)
T011: Q#3: Consider a metallic sphere carrying a charge of 4.0*10**(-8) C and having a potential of 400 v. Find the
diameter of the sphere. (Ans:6.0 m.)
Q#9: Two equal charges, each of 0.12 C, are separated by a distance of 1.8 m. What is the work done, by an external agent,
to bring a charge of 0.15 C from infinity to the midpoint between the two charges? (Ans: 3.6*10**8 J.)
Q#12: What is the electric potential energy of an electron at a distance r = 2.40*10**(-10) m from the nucleus of a hydrogen
atom? (the nucleus consists of a single proton) (Ans: -6.0 eV.).
T002:Q#1:
A particle [m = 8.0*10**(-9) kg, q = +6.0*10**(-9) C] has a speed of 80 m/s at point A and moves to point B
where the potential is 2.0*10**3 V greater than at point A. What is the particle's kinetic energy at point B? (Assume that only
electric forces act on the particle during its motion.) (Ans:14*10**(-6) J.)
Q#2: In figure 2, four charges are fixed at the corners of a square whose sides are of length d. The work done by an external
agent to bring a fifth charge, Q, from infinity to the center of the square is:
(Ans: - 2.8*k*q*Q/d.)
Q#3: A charge q is located at the center of a circle with a large radius R, see figure 4. Another charge Q is located on the
circumference of the circle at the x-axis. What is the work, in Joules, needed to move Q from its location to point F, on the xaxis, along the circumference? (Ans: Zero.)
T001:Q#1:
Two point charges Q1 and Q2 are positioned as shown in Figure (2) .If Q1 = 2.0*10**(-9) C, Q2 = 2.0*10**(-9) C, a = 3.0 m, and b = 4.0 m, what is the electric potential difference, VA- VB? (Ans: 4.8 V)
Q#2: A particle [m = 8.0*10**(-9) kg, q = +6.0*10**(-9) C] has a speed of 80 m/s at point A and moves to point B where
the potential is 2.0*10**3 V greater than at point A. What is the particle's kinetic energy at point B? (Assume that only
electric forces act on the particle during its motion.) (Ans: 14*10** (-6) J.)
Q#3: A 2 meters conducting rod is fixed perpendicularly to a uniform 200 Nlc electric field. The potential difference
between its ends is: (Ans: Zero.)
244
Q#4: Two conducting spheres are very far apart. The smaller sphere carries a total charge of 6 micro-C. The larger sphere has
a radius twice that of the smaller sphere and is neutral (Q = 0) .After the two spheres are connected by a thin conducting wire,
the charges on the smaller and the larger spheres, respectively are: (Ans: 2 micro-C and 4 micro-C.)
U(J)
1.5*10-16
4 μC
3 cm
0
0
0.02
x(m)
2 μC
Figure 5
8 μC
4 cm
Figure 5, T042
Fig. 3, T062
245