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Pavitra Gupta 9312281591
Pavitra Gupta 9312281591
ELECTRIC CHARGES and COULOMB’S LAW
Q.1
Two charged particles placed at a distance of 1cm. What can be the minimum force between them?
[2.3 x 10-24N]
Q.2
Two positive point charges 0.1m apart repel each other by a force of 18 N. If the sum of two charges is
9 C, find the charges.
Q.3
[5C, 4C]
Two free point charges +4q and +q are at a distance of ‘a’. Where should a third point charge Q be
placed between them so that the entire system is in equilibrium? What will be the magnitude and sign of
Q?
Q.4
[Q= - 4q/9 at 2a/3 from +4q]
Two particles, each having a mass of 5g and charge 10-7 C, stay in limiting equilibrium on a horizontal
table with a separation of 10cm between them. The coefficient of friction between each particle and the
table is same. Find the value of this coefficient.
Q.5
[=0.18]
Two similarly and equally charged identical metal spheres A and B repel each other with a force of 2 x
10-5 N. A third identical, uncharged sphere C is touched with A and then placed at the mid point
between A and B. What is the net electric force on C?
Q.6
[2 x 10-5 N towards A]
Charges q1 = +1.5 mC, q2 = +0.2 mC and q3 = – 0.5mC are placed at points A, B and C respectively of a
triangle right angled at B. If AC = 1.2m and BC = 0.6m, calculate magnitude of resultant force on q2.
[3125 N]
Q.7
Two opposite corners of a square carry Q charge each and the other two opposite corners of the same
square carry q charge each. If the resultant force on q is 0, how are Q and q related?
Q.8
[q = - 2 2 Q]
A pith ball A of mass 9 x 10-5 kg carries a charge of 5 C. What must be the magnitude and sign of the
charge on another ball B held 2 cm above ball A, such that A remains suspended stationary above the
[7.84x10-12C]
ground?
Q.9
Two point charges of 6.5 x 10-7 C each are separated by a distance of 50 cm. What is the force of
repulsion between them if
(i) they are placed in air?
(ii) they are placed in water?
[1.521 N, 0.019 N]
Q.10
Four point charges 2C, –5 C, 2 C and –5 C are placed at the corners A, B, C and D respectively, of
a square ABCD of side 10 cm. Find the force on a charge of 1 C placed at the centre O of the square.
Q.11
A polythene piece rubbed with wool is found to have a negative charge of 3 x 10-7 C. (i) Find the
number of electron transferred and state whether electrons are transferred from wool to polythene or
[2x1012 from wool to polythene, yes]
otherwise. (ii) Is there a transfer of mass?
Q.12
Calculate the force between 2 alpha particles separated by a distance of 1.6 x 10-15 m. [360 N repulsive]
Q.13
Three equal charges, 2.0 x 10-6 C each, are held fixed at the three corners of an equilateral triangle of
side 5 cm. find the coulomb force experienced by one of the charges due to the rest two.
[14.4 N at 30 with a side of ]
Pavitra Gupta 9312281591
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Pavitra Gupta 9312281591
Pavitra Gupta 9312281591
Pavitra Gupta 9312281591
ELECTRIC FIELD
Q.1
Q.2
A test charge 2nC, placed at origin, experiences a force of 8 x 10-4 N in the positive y – direction. Find
electric field at origin. What would be the force on charge – 4nC placed at origin?
[4x105 N/C, -16x10-4 N]
Find the magnitude of electric field which can balance a deuteron of mass 3.2 x 10-27 kg.
[19.6x10-8N/C]
Q.3
A charged particle of mass 1.0 g is suspended through a silk thread of length 40 cm in a horizontal
electric field of 4.0 x 104 N/C. If the particle stays at a distance of 24 cm from the vertical line passing
through its point of suspension, find the charge on the particle.
[1.8 x 10-7 C]
Q.4
ABC is an equilateral triangle of side 5 cm. Two charges  50/3 x 10-3 C are placed at A & B
respectively. Calculate magnitude and direction of field at C.
[6 x 104 N/C, ║ to AB]
Q.5
Two charges  10 C are held at 5 mm apart. Calculate their dipole moment. What is the electric field
intensity at a distance of 15 cm from the centre of dipole on its axial line?
[5 x 10-8 Cm, 2.7 x 105 N/C]
An electric dipole of length 2 cm is placed with its axis making an angle of 30 with a uniform electric
field of 105 N/C. If it experiences a torque of 10 3 Nm, calculate (i) magnitude of charges on dipole
(ii) potential energy of dipole.
[1.732 x 10-2C, - 4.64 J]
Q.6
Q.7
In a certain region of space, electric field is along the positive z – direction whose magnitude increases
uniformly at the rate of 105 N/Cm along the positive z – direction. What are the forces and torque
experienced by dipole of dipole moment 10-7 Cm in the negative z – direction?
[-10-2 N, 0]
Q.8
An oil drop of 12 excess electron is held stationary under a constant electric field 2.55 x 104 V/m in
Milikan’s oil drop experiment. The density of oil is 1.26 g/cm3. Find the radius of the drop.
(Take g = 9.81 m/s2)
[9.81 x 10-4mm]
Q.9
A copper ball of density 8.6 g/cm3, 1 cm in diameter is immersed in oil of density 0.8 g/cm3. If the ball
remains suspended in oil in an electric field of 36000 N/C acting in upward direction, what is the charge
on the ball?
Q.10
Calculate the electric field intensity at point P ( 0, 3, -1 ) due to a charge of – 2 C placed at point
3
A ( -3, 0, -4 ).
[  2 3  10 ( ˆi  ˆj  k̂) N/C]
9
Q.11
A charge 4 x 10-9 C is distributed uniformly on a ring of radius 0.3 m. Find field intensity at a point on
the axis of ring at 0.4 m from centre and also at the centre.
[115.2N/C, 0]
Q.12
Two point charges of +3 x 10-19 C and + 12 x 10-19 C are separated by a distance of 2.5 m. Find the
point on the line joining them at which the electric field intensity is zero.
[5/6 m from 3 x 10-19 C]
Q.13
Two point charges 3C and – 3 C are located 20 cm apart in vacuum at point A and B respectively. (i)
What is the electric field at the mid point O of the line AB. (ii) If a negative charge of magnitude
1.5 x 10-9 C is placed at this point, what is the force experienced by this charge?
[5.4x106 N/C along OB,8.1x10-3N along OA]
Two charges  10C are placed 5 mm apart. Find the electric field at (i) point P on the axis of the dipole
15 cm away from its center O on the side of positive charge, (ii) point Q, 15 cm away from O on a line
passing through O and normal to axis of the dipole.
[2.7x105N/C along BP,1.33x105N/C along BA]
Q.14
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ELECTRIC POTENTIAL and ELECTRIC FLUX
Q.1
The electric field and potential at a point due to a point charge are 30 N/C and 15 J/C respectively. Find
the distance of point from the charge and the magnitude of the charge.
[0.5 m, 0.833 x 10-3 C]
Q.2
If 100 J of work is done to move a charge of 4 C from a place of potential – 10 volt to another place
where potential is V volt, find the value of V.
[15 V]
Q.3
An electric field of 20 N/C exists along x – axis. Calculate potential difference VB – VA where
coordinates of pints A and B are ( 4m, 2m ) and ( 0, 0 ) respectively.
[80 V]
Q.4
A point charge 10-8 C is situated at origin. Find the potential difference between points A( 4, 4, 2 ) and
B(1, 2, 2 ).
[-15 V]
Q.5
Two positive point charges 10 C and 5 C are 1 m apart. Find the work done in bringing them 0.5 m
apart.
[0.45 J]
Q.6
Two electrons, each with a velocity of 106 m/s are released towards each other. What will be the closest
distance of approach between them?
[2.56 x 10-10 m]
Q.7
Two identical particles, each of mass 10 g and carrying charge 2 x 10-4 C, are kept at a distance of 10
cm and released. What would be the speed of particles, when separation becomes infinitely large?
[600 m/s]
An infinite thin plane sheet of charge density 10-8 C/m2 is held in air. How far apart are two
equipotential surfaces, whose potential difference is 5 V?
[8.85 x 10-3 m]
Q.8
Q.9
(a) A rectangular frame of wire 25 cm x 15 cm is placed in uniform electric field of 2 x 104 N/C such
that the plane of frame is normal to the field. Find electric flux linked with the frame.
(b) Find electric flux if this frame is converted into a square.
[750 Vm; 800Vm]
Q.10
(a) A box encloses an electric dipole of charges  5C and length 10 cm. What is the total electric flux
through the box?
(b) If the number of electric field lines from a closed surface are 1000, calculate the charge enclosed by
the surface.
[0; 8.85 x 10-9 C]
Q.11
The electric field is ( 5 î  4 ˆj  4 k̂ )  10 N/C in a region. Calculate electric flux due to this field over
an area of ( 2 î  ˆj )  10 -2 m2.
[6000 Nm2/C]
5
If the potential in the region of space around point ( –1m, 2m, 3m ) is V = (10 x2 + 5 y2 – 3 z2 ) volts,
calculate the three components of electric field at this point.
[Ex = 20V/m; Ey = -20 V/m; Ez=18 V/m]
Q.13 An electric dipole consists of charges of 2 x 10-8 C separated
by a distance of 2 mm. It is placed near a long line charge of
density 4 x 10-4 C/m as shown in the figure, such that
negative charge is 2 cm from the line charge.
-q
+q
Find the force acting on the dipole.
Line charge
Q.12
2 cm
[0.66 N]
Pavitra Gupta 9312281591
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Pavitra Gupta 9312281591
Pavitra Gupta 9312281591
Pavitra Gupta 9312281591
CAPACITANCE
Q.1
A spherical conductor has a surface charge density of 0.07 C/m2. When charge is increased by 4.4 C the
density changes by 0.084 C/m2. Find the radius & initial charge.
[2.04 m; 11/3 C]
Q.2
If 64 small mercury drops each charged to 220 V coalesce, what is the potential of the bigger drop?
[3520V]
Q.3
At what distance should the plates of area 0.2 m x 0.1 m of air capacitor be placed in order to have a
capacitance as a spherical conductor of radius 0.5 m?
[3.18 mm]
Q.4
A parallel plat air capacitor having plate area 6 x 10-3 m2 and plate separation 3 mm is connected to 100
V supply. Calculate charge on each plate. Explain what would happen when a 3 mm thick mica sheet
( = 6 ) is inserted between plates (a) while voltage supply remains connected (b) after supply is
connected?
[1.77 x 10-9 C; 1.06 x 10-9 C; V=16.7 V]
Q.5
Calculate the value of C for the given figure,
if equivalent capacitance between
P and Q is 30 F.
[60F]
20F
20F
P
Q
C
20F
Q.6
What is the capacitance of arrangement of 4 plates each of area A at a distance d in air for the given
figure?
d
d
A
(i) A
B
(ii)
d
d
[20A/d]
B
d
[30A/d]
Q.7
A parallel plate capacitor is filled with two dielectrics as shown in the figures. Calculate the capacity of
each.
(i)
(ii)
[
Q.8
0A
( 1   2 ) ]
2d
Calculate the equivalent capacitance
between A and B for the following figure:
[
2  0 A  1 2
]
d ( 1   2 )
A
B
5F
10F
15F
30F
[15F]
4 F
Q.9
Q.10
Q.11
Q.12
Take potential of B to be zero in the given figure.
(a) Find potential at C & D.
(b) If a capacitor is placed between C and D,
what charge will appear on this capacitor?
[50/3 V;50/3 V; 0]
C
8 F
A
B
3 F
D
6 F
50 V
A 4 F capacitor is charged by 200 V supply. It is disconnected from supply and connected to another
uncharged 2 F capacitor. How much electric energy is lost by first capacitor?
[2.67 x 10-2 J]
A capacitor of 20 F and charged to 500 V is connected in parallel with another 10 F capacitor
charged to 200 V. Find the common potential.
[400 V]
Two capacitors of capacitances C1 = 3 F and C2 = 6 F arranged in series are connected in parallel
with 3rd capacitor C3 = 4 F. The arrangement is then connected to 6 V battery. Find total energy stored
in the arrangement.
[1.08 x 10-4 J]
Pavitra Gupta 9312281591
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Pavitra Gupta 9312281591
Q.13
Pavitra Gupta 9312281591
In Van de graf generator, spherical shell of metal has 15 x 105 V potential. The dielectric strength of
surrounding gas is 5 x 107 V/m. Find the minimum radius of the shell.
[0.3 m]
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Pavitra Gupta 9312281591