Electric Field and Charges Worksheet 02

ELECTRIC FIELD AND CHARGES WORKSHEET-02
1. Two point charges q1 and q2 are located with points having position vectors r1 and r2 .
(i) Find the position vector r3 where the third charge q3 should be placed so that force
acting on each of the three charges would be equal to zero.
(ii) Find the amount of charge q3
2. Find the magnitude of electric field strength on the axis of the ring as a function of distance x from
its centre.
3. Two equally charged metal balls each of mass m Kg are suspended from the same point by two
insulated threads of length l m long. At equilibrium, as a result of mutual separation between
balls, balls are separated by x m. Determine the charge on each ball.
4. There are two identical particles each of mass m and carrying charge Q. Initially one of them is at
rest and another charge moves with velocity v directly towards the particle at rest. Find the
distance of closest approach.
5. Two opposite corners of square carry charge –q and other tow opposite corners of same square
carry charge +q as shown below in the figure
6. All the four charges are equal in magnitude. Find the magnitude and direction of force on the
charge on the upper right corner by the other three charges.
An electric dipole is placed at a distance x from a infinitely long rod of linear charge
density λ.
(i) Find the net amount of force acting on the dipole.
(ii) Assuming that dipole is fixed at its centre find its time period of oscillations if the dipole is slightly
rotated about its equilibrium position.
7. Consider the figure given below
A positive charge +q is placed at corner of the cube. Find the electric flux
through the right face BCGDB of the cube.
8. Consider a sphere of radius r having charge q C distributed uniformly over the sphere. This
sphere is now covered with a hollow conducting sphere of radius R>r.
(i) Find the electric field at point P away from the centre O of the sphere such that r<OP<R.
(ii) Find the surface charge density on the outer surface of the hollow sphere if charge q’ C is placed
on the hollow sphere.
9. Figure shows three point charges, +2q, -q and + 3q. Two charges +2q and -q are enclosed within
a surface ‘S’. What is the electric flux due to this configuration through
the surface ‘S’
10. Two charges of magnitudes -3Q and + 2Q are located at points (a, 0) and (4a, 0) respectively.
What is the electric flux due to these charges through a sphere of radius ‘5a’ with its centre at the
origin?
11. What is the electric flux through a cube of side 1 cm which encloses an electric dipole?
12. A point charge +Q is placed in the vicinity of a conducting surface. Draw the electric field lines
between the surface and the charge.
13. A spherical conducting shell of inner radius rx and outer radius r2 has a charge ‘Q’. A charge ‘q’ is
placed at the centre of the shell.
(a) What is the surface charge density on the
(i) inner surface,
(ii) outer surface of the shell?
14. Plot a graph showing the variation of Coulomb force (F) versus (1/r2), where r is the distance
between the two charges of each pair of charges: (1µC, 2µC) and (2µC, – 3µC). Interpret the
graphs obtained.
A hollow cylindrical box of length 1m and area of cross-section 25 cm2 is placed in a three dimensional
coordinate system as shown in the figure. The electric field in the region is given by E→=50xi^ where E is
in NC-1 and x is in metres. Find
(i) Net flux through the cylinder.

(ii) Charge enclosed by the cylinder.
15. Given a uniform electric field E= 2 × 103 i^ N/ C, find the flux of

this field through a square of side 20 cm, whose plane is parallel to the y-z plane. What would be
the flux through the same square, if the plane makes an angle of 30° with the x-axis?
16. A small metal sphere carrying charge +Q is located at the centre of a spherical cavity in a large
uncharged metallic spherical shell. Write the charges on the inner and outer surfaces of the shell.
Write the expression for the electric field at the point P1
17. A sphere S1 of radius r1 encloses a net charge Q. If there is another concentric sphere S2 of
radius r2 (r2 > r,) enclosing charge 2Q, find the ratio of the electric flux through S1 and S2. How will
the electric flux through sphere S1 change if a medium of dielectric constant K is introduced in the
space inside S 2 in place of air?
18. Two point charges + q and -2q are placed at the vertices ‘B’ and ‘C’ of an equilateral triangle ABC
of side as given in the figure. Obtain the expression for (i) the magnitude and (ii) the direction of
the resultant electric field at the vertex A due to these two charges.
19. The electric field components due to a charge inside the cube of side 0.1 m are as shown :
Ex = ax, where α = 500 N/C-m
Calculate
(i) the flux through the cube, and
(ii) the charge inside the cube.

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ELECTRIC FIELD AND CHARGES WORKSHEET-02

the surface ‘S’

(i) Net flux through the cylinder.

15. Given a uniform electric field E= 2 × 103 i^ N/ C, find the flux of

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