1. Figure shows two charge particles on an axis. The charges are free to move. At one point, however, a third charged particle can be placed such that all three particles are in equilibrium.
(a) Is that point to the left of the first two particles, to their right, or between them?
(b) Should the third particle be positively or negatively charged?
(c) Is the equilibrium stable or unstable?
2. In figure, a central particle of charge –q is surrounded by two circular rings of charged particles, of radii r and R, with R >r . What is the magnitude and direction of the net electrostatic force on the central particle due to the other particles?
3. Figure shows four situations in which particles of charge +q or –q are fixed in place. In each, the particles on the
x -axis are equidistant from the y-axis. The particle on y-axis experiences an electrostatics force F from each of these two particles.
Electrostatics: Part 1 69
(a) What are the signs of each of the three charges?
Explain your reasoning.
(b) At what point(s) is the magnitude of the electric field the smallest? Explain your reasoning. Explain how the fields produced by each individual point charge combine to give a small net field at this point or points.
(c) Two point chargesq and –q are placed at a distanced
apart. What are the points at which resultant electric field is parallel to the line joining the two charges?
9. Two point chargesQ and 4Q are fixed at a distance of 12 cm from each other. Sketch lines of force and locate the neutral point, if any.
10. Is an electric field of the type shown by the electric lines in figure physically possible?
11. Which of the following statement is correct? If E = 0, at all points of a closed surface:
(a) The electric flux through the surface is zero.
(b) The total charge enclosed by the surface is zero.
12. A hollow dielectric sphere as shown in the figure has inner and outer radii of R1 and R2 respectively. The total charge carried by the sphere is +Q, this charge is uniformly distributed between R1 and R2. Then
(a) the electric field forr< R1 is zero.
(b) the electric field for R1 < r < R2 is given by
………
(c) the electric field forr > R2 is given by……….
13. Three identical positive charges Q are arranged at the vertices of an equilateral triangle. The side of the triangle isa. Find the intensity of the field at the vertex of a regular tetrahedron of which the triangle is the base.
14. Two point charges of +5 × 10–19 C and +20 × 10–19 C are separated by a distance of 2 m. The electric field intensity will be zero at a distanced = ... from the charge of 5
× 10–19 C.
15. An electron (mass me) falls through a distance ‘d ’ in a uniform electric field of magnitude E .
The direction of the field is reversed keeping its magnitude unchanged and a proton (massm p) falls through the same distance. If the time taken by electron and proton to fall the distanced is ‘t electron’ and ‘t proton’ respectively, then the ratio electron =
proton t
t ...
16. Two charged metal plates in vacuum are 10 cm apart. A uniform electric field of intensity (45/16) × 103 N/C–1is applied between the plates. An electron is released between the plates from rest at a point just outside the negative plate.
Calculate:
(i) How long (t ) will electron take to reach the other plate?
(ii) At what velocity (v) will it be going just before it hits the other plate?
17. A ring of diameterd is rotated in a uniform electric field until the position of maximum electric flux is found. The flux is found to bef . What is the electric field strength?
18. Two point electric charges of unknown magnitudes and signs are placed a certain distance apart. The electric field intensity is zero at a point not between the charges but on the line joining them. Write two essential conditions for this to happen.
19. A dipole consists of two particles carrying charges +2m C and −2m C and masses 1 kg and 2 kg, respectively, separated by a distance of 6 m. It is placed in a uniform electric field of 8×104 V/m–1. For small oscillations about its equilibrium position, find the angular frequency.
20. A small electric dipole of dipole momentP is placed near a point charge +Q as shown. Then the net force on the dipole is towards …….
70 Electrostatics: Part 1
21. In defining electric field due to a point charge, the test charge has to be vanishingly small. How this condition can be justified, when we know that charge less than that on an electron or a proton is not possible?
22. Two point electric charges of unknown magnitude and sign are placed a distance apart. The electric field intensity is zero at a point not between the charges but on the line joining them. Write two essential conditions for this to
happen.
23. What is the ratio of the strength of electric field at a point on axial line and at a point at same distance on equatorial line of an electric dipole of very small length?
24. The distance of the field point on the equatorial plane of a small electric dipole is halved. By what factor will the electric field due to the dipole change?
25. Define intensity of electric field at a point. At what points is the electric dipole field intensity parallel to the line joining the charges?
Or
Two point charges +q and –q are placed at a distance d
apart. What are points at which the resultant field is parallel to the line joining the two charges?
26. Can two balls having same kind of charge on them attract each other? Explain.
27. Force of attraction between two point electric charges placed at a distance d in a medium is F . What distance apart should these be kept in the same medium, so that force between them becomesF /3?
28. S 1 and S 2 are two hollow concentric spheres enclosing chargesQ and 2Q respectively as shown in figure. What is the ratio of the electric flux throughS 1 andS 2?
29. A small conducting spherical shell with inner radius a
and outer radiusbis concentric with a larger conducting spherical shell with inner radiuscand outer radiusd. The inner shell has total charge +2q and the outer shell has charge +4q.
(a) Make a plot of the magnitude of the electric field vs.
r ………..
(b) Calculate the electric field (magnitude and direction) in terms of q and the distance r from the common centre of the two shells for
(i) r<a; (ii) a<r <b; (iii) b <r <c; (iv)c <r <d ; (v) r >d .
Show your results in a graph of the radial component of
Æ
E as a function ofr .
(c) What is the total charge on the (i) inner surface of the small shell;
(ii) outer surface of the small shell;
(iii) inner surface of the large shell;
(iv) outer surface of the large shell ?
30. Which of the following statements is/are correct?
(a) Electric field calculated by Gauss law is the field due to only those charges, which are enclosed inside the Gaussian surface.
(b) Gauss law is applicable only when there is a symmetrical distribution of charge.
(c) Electric flux through a closed surface is equal to total flux due to all the charges enclosed within that surface only.
Electrostatics: Part 1 71
STATE LEVEL EXERCISES
attraction, while pairs (2, 3), (4, 5) show repulsion.
Therefore ball 1 must be
(a) neutral (b) made of metal
(c) positively charged (d) negatively charged
8. There are two charges +1 micro coulomb and 5 micro coulomb. The ratio of the forces acting on them will be
(a) 1 : 1 (b) 1 : 25
(c) 1 : 5 (d) 5 : 1
9. An electric chargeq exerts a forceF on a similar electric chargeq separated by a distance r . A third chargeq /4 is placed mid-way between the two charges. Now, th e force
F will….
10. A charged particle moves with a speed v in a circular path of radius R around a long uniformly charged conductor
(a) v µR (b) µ
(d) v is independent of R 11. A positive point chargeQ is brought near an isolated metal
cube
(a) The cube becomes negatively charged
(b) The cube becomes positively charged
(c) The interior becomes positively charged and the surface becomes negatively charged
(d) The interior remains charge free and the surface gets non-uniform charge distribution
12. A simple pendulum of time periodT is suspended above a large horizontal metal sheet with uniformly distributed positive charge. If the bob is given some negative charge, its time period of oscillation will be
(a) >T (b) <T (c) T
(d) proportional to its amplitude
13. Charge Q is divided into two parts which are then kept some distanced apart. The force between them will be maximum if the two parts are
(a) Q /2 each
(b) Q /4 and 3Q /4
(c) Q /3 and 2Q /3
(d) e and (Q-e), wheree = electronic charge
14. Two chargesq1 andq2 separated by a dielectric of dielectric constant 4 repel each other with a force of 10 N. Another
S
INGLEC
ORRECTA
NSWERT
YPE1. Two identical metal balls with charges +2Q and −Q are separated by same distance, and exert a forceF on each other. They are joined by a conducting wire, which is then removed. The force between them will now be
(a) F (b) F /2
(c) F /4 (d) F /8
2. A cube of side ‘b’ has charge ‘q’ at each of its vertices.
The electric field at the centre of the cube will be
(a) 2
3. Three small spheres, each carrying a positive charge Q, are placed on the circumference of a circle of radius ‘r ’ to form an equilateral triangle. The electric field intensity at the centre of the circle will be
(a) 3Q
4. Two similar conducting spheres A and B are brought in contact and insulated from earth. A negatively charged ebonite rod is brought near A. Now
(a) A will have +ve charge and B will have –ve charge.
(b) A will have –ve charge and B will have +ve charge.
(c) Both will acquire negative charge.
(d) Both will remain uncharged.
5. Two identical metallic spheres X and Y have exactly equal masses. X is given a positive charge q coulomb and Y is given an equal negative charge. Then after charging.
(a) Masses of X and Y are equal
(b) Mass of Y is greater than X
(c) Mass is not involved
(d) Mass of X is greater than Y
6. A chargeq1 exerts some force on a second chargeq2. If a third chargeq3 is brought near, then the force ofq1 exerted onq2
(a) will increase in magnitude
(b) will decrease in magnitude
(c) will remain unchanged
(d) will increase ifq3is of the same sign as q1 and will decrease ifq3is of opposite sign
7. Five balls numbered (1 to 5 are suspended using separate threads. Pairs (1, 2), (2, 4) and (4, 1) show electrostatic
72 Electrostatics: Part 1
chargeq3 is placed betweenq1 andq2 such that the distance ofq3 fromq1 is 1/4 times the distance ofq3 fromq2. Now, the force of repulsion betweenq1 andq2 is
(a) 10 N (b) 10q1
(b) –ve direction ofY -axis
(c) +ve direction of Z-axis
(d) –ve direction of Z-axis
16. An uncharged metal object M is insulated from its surroundings. A positively charged metal sphereS is then brought near to M . Which diagram best illustrates the resultant distributions of charge onS and M ?
(a) (b)
(c) (d)
17. A thin metallic spherical shell contains a charge Q on it.
A point charge q is placed at the centre of the shell and another chargeq1 is placed outside it as shown in the figure.
All the three charges are positive.
The force on the charge at the centre is
(a) towards left (b) towards right
(c) upward (d) zero
18. Three small spheres, each carrying a charge q are placed on the circumference of a circle of radius R, forming an equilateral triangle. If we place another charge Q at the centre of the circle, then the force onQ will be
(a) zero (b) 2 equilateral triangle. Assuming only electrostatic forces are acting:
(a) the system can never be in equilibrium
(b) the system will be in equilibrium if the charges rotate about the centre of the triangle
(c) the system will be in equilibrium if the charges have different magnitudes and different signs
(d) the system will be in equilibrium if the charges have the same magnitude but different signs
20. A point charge A of charge +4mC and another point charge
B of charge –1mC are placed in air at a distance 1 metre apart. Then the distance of the point on the line joining the charges and from the charge B, where the resultant electric field is zero, is (in metre)
(a) 1.5 (b) 0.5
(a) execute simple harmonic motion about the origin
(b) move to the origin and remain at rest
(c) move to infinity
(d) execute oscillatory but not simple harmonic motion
22. Three charges 4q,Q andq are placed in a straight line of lengthl at point 0, l/2 and l respectively. What should be
Q in order in make the net force onq to be zero?
(a) −q (b)
- 1 2q
(c) −2q (d) 4q
23. In a regular polygon ofn sides, each corner is at a distance
r from the centre. Identical charges of magnitude q are placed at (n – 1) corners. The field at the centre is
24. A charge Q is placed at each of two opposite corners of a square. A chargeq is laced at each of the two opposite corners of the square. If the resultant electric field onQ is zero, then
(a) =
-2 -2
Q q (b) Q = -2 2q
(c) Q = –2q (d) Q = 2 2q
25. The charge per unit length of the four quadrant of the ring is 2l , –2l ,l and –l respectively. The electric field at the centre is
Electrostatics: Part 1 73
26. Two identical positive charges are fixed on the y-axis. At equal distance from the origin O. A negatively charged particle starts on the x -axis at a large distance from O, moves along the x -axis, passes throughO and moves for away fromO. Its accelerationa is taken as positive along its direction of motion. The particle’s acceleration a is plotted against its x -coordinate. Which of the following best represents the plot? radiusr around an infinitely long line of charge of linear charge density +l . Then time period will be:
(a) = p are placed at a distance R from each other. The maximum force of repulsion between them will occur, when
[EAMCET 2011]
2. An isolated solid metallic sphere is given +Q charge. The charge will be distributed on the sphere[MH CET 2011]
(a) Uniformly but only on surface
(b) Only on surface but non-uniformly
(c) Uniformly inside the volume
(d) Non-uniformly inside the volume
3. Two small spheres each having the charge +Q are suspended by insulating threads of length L from a hook. This arrangement is taken in space where there is no gravitational effect, then the angle between the two suspensions and the tension in each will be
[KCET 2011]
74 Electrostatics: Part 1
5. Five balls numbered 1 to 5 are suspended using separate threads. Pairs (1, 2), (2, 4) and (4, 1) show electrostatic attraction, while pair (2, 3) and (4, 5) show repulsion.
Therefore ball 1 must be [UP SEAT 2012]
(a) Positively charged
(b) Negatively charged
(c) Neutral
(d) Made of metal
6. Equal chargesq are placed at the four corners A,B,C,D of a square of length a. The magnitude of the force on the
charge at Bwill be [EAMCET 2012] induced charge in the aluminum will be[MP CET 2012]
(a) Zero
(b) Greater than in copper
(c) Equal to that in copper
(d) Less than in copper
8. When a body is earth connected, electrons from the earth flow into the body. This means the body is…..
[KCET 2012]
(a) Unchanged (b) Charged positively
(c) Charged negatively (d) An insulator
9. The charges on two sphere are +7m C and – 5m C respectively.
They experience a force F . If each of them is given and additional charge of – 2m C , the new force of attraction will
be [MH CET 2013]
(a) F (b) F / 2
(c) F / 3 (d) 2F
10. The ratio of electrostatic and gravitational forces acting between electron and proton separated by a distance 5 × 10–11m, will be (Charge on electron = 1.6 × 10–19 C, mass additional charge –6 × 106 C, the force between them will
be [KCET 2013] fixed with a distance ‘r ’ between them. A third identical, but uncharged sphereC is brought in contact with A and then placed at the mid-point of the line joining A and B. The magnitude of the net electric force onC is
[UPSEAT 2014]
(a) F (b) 3F /4
(c) F /2 (d) F /4
13. Two charges of equal magnitudes and at a distancer exert a forceFon each other. If the charges are halved and distance between them is doubled, then the new force acting on each
charge is [MH CET 2014]
(a) F / 8 (b) F / 4
(c) 4F (d) F / 16
14. An infinite number of charges, each of charge 1 mC, are placed on the x -axis with co-ordinates x = 1, 2, 4, 8, ....• . If a charge of 1 C is kept at the origin, then what is the net force acting on 1 C charge? [EAMCET 2014]
(a) 9000 N (b) 12000 N
(c) 24000 N (d) 36000 N
15. The number of electrons in 1.6 C charge will be
[MPPET 2014]
(a) 1019 (b) 1020
(c) 1.1 × 1019 (d) 1.1 × 102
16. Four metal conductors having different shapes
[Kerala 2015]
1. A sphere 2. Cylindrical
3. Pear 3. Lightning conductor
are mounted on insulating stands and charged. The one which is best suited to retain the charges for a longer time
is [KCET 2014]
(a) 1 (b) 2
(c) 3 (d) 4
17. Identify the wrong statement in the following. Coulomb’s law correctly describes the electric force that
[WB JEE 2015]
(a) Binds the electrons of an atom to its nucleus
(b) Binds the protons and neutrons in the nucleus of an atom
Electrostatics: Part 1 75
(c) Binds atoms together to form molecules
(d) Binds atoms and molecules together to form solids
18. A cylinder of radius R and length L is placed in a uniform electric field E parallel to the cylinder axis. The total flux for the surface of the cylinder is given by
EAMCET 2015]
(a) 2p R2 E (b) p R2 / E (c) (p R2 –p R)/ E (d) Zero
19. Total electric flux coming out of a unit positive charge put
in air is [KCET 2015]
(a) e 0 (b) e 0–1
(c) (4pe 0)–1 (d) 4pe 0
20. Eight dipoles of charges of magnitudee are placed inside a cube. The total electric flux coming out of the cube will
be [MP PET 2015]
L. The electric flux emerging from the cube is
[UPSEAT 2016] cylindrical vessel. The flux of the electric field through the surface of the vessel is [EAMCET 2016]
(a) Zero (b)
23. According to Gauss’ theorem, electric field of an infinitely long straight wire is proportional to [MH CET 2016]
(a) r (b) 12 straight wire of radius 1 mm. The charge per cm length of the wire isQ coulomb. Another cylindrical surface of radius 50 cm and length 1 m symmetrically encloses the wire as shown in the figure. The total electric flux passing through the cylindrical surface is [MP PET 2016]
(a) shown in the figure andS is a spherical Gaussian surface of radius R. Which of the following is true according to
the Gauss’s law? [KCET 2016]
(a) 1 2 3 1 2 3
76 Electrostatics: Part 1
JEE EXERCISES
5. The figure shows four chargesq1,q2,q3,q4 fixed in space.
Then the total flux of electric field through a closed surface
S , due to all chargesq1,q2,q3 andq4 is
(a) not equal to the total flux throughS due to chargesq3
andq4
(b) equal to the total flux throughS due to chargesq3 and
q4
(c) zero ifq1 +q2 =q3 +q4
(d) twice the total flux throughS due to charges q3 and
q4 ifq1 +q2 =q3 +q4
6. Three charges of q1 = 1 × 10–6 C, q2 = 2 × 10–6 C and
q3 = –3 × 10–6 C have been placed as shown. Then the net electric flux will be maximum for the surface
(a) S 1 (b) S 2
(c) S 3 (d) same for all three
7. Two charges q and –4q are held at a separation r on a frictionless surface. Another charge is kept in such a way that they do not move if released. The value of the third charge and its position from –4q is
(a) –2q, 2r (b) –4q, 2r
(c) q,r (d) 4q, 2r
8. An electron of massme, initially at rest, moves through a certain distance in a uniform electric field in time t 1. A proton of mass mp, also, initially at rest, takes time t 2 to move through an equal distance in this uniform electric field. Neglecting the effect of gravity, the ratio t 2 / t 1 is nearly equal to
(a) 1 (b) (mp / me)1/2
(c) (me / mp)1/2 (d) 1836
9. Four point charges are placed at the corners of a square with diagonal 2a as shown. What is the total electric field at the centre of the square?