Chapter Practice Problems FIITJEE

CHENNAI CENTRE

Subject: Physics Topic: ELECTROSTATICS

NAME:

FIITJEE CHENNAI CENTRE. 175 Poonamallee High Road. Opp. Ega Theatre, Kilpauk. Chennai-10 PH: 044 - 42859701

1. Three identical positive charges Q are placed on the verticals of a equilateral triangle. The side of the triangle is a .

Find the field intensity at the vertex of the tetrahedron with triangle as the base.

2. The curved wire which is a part of a circle of radius ‘r’ has a charge per unit length

sin 2oλ λ θ= where θ is as shown. Calculate the net charge on the ring and the electric field intensity at point O, the centre of the circle.

r

θ

3. An infinitely long string uniformly charged with a linear density λ and a segment of length ℓ uniformly charged with linearly density 2λ lie in a plane of right angles at each other and separated by a distance or . Determine the force

with which these two interact

4. The intensity of an electric field depends only on the co – ordinate x and y as ( )2 2

ˆ ˆa xi yjE

x y

+=

+

�� where a is constant.

Find the charge within a sphere of radius R with the centre at the origin

5. An electric field line emerges from a positive point charge 1q+ at angle

α to the straight line connecting to a negative point charge 2q . At

what angle β will the field line enter the charge 2q−

α β

2q− 1q+

6. Two charged rings of radius R are at a distance R apart as shown in figure.

(i) If the charge of each ring is Q what is E along the x – axis as a

function of R, Q, x

(ii) If the charge on the left ring is 1Q and on the right is 2Q . Find the

work done is moving point charge q from the centre of the left ring to

the right ring

R

Y

X

R

7. The potential of a field inside a charge sphere depends only on the distance ‘r’ for its centre to the points under

consideration as 2V ar b= + where a & b are constants. Find the distribution ( )Vρ within the sphere

8. Determine the force F of interaction between two hemispheres of radius ‘R’ touching each other along the equator if

one of hemisphere is uniformly charged with a surface density σ and other with same surface density σ

9. A solid insulating sphere of radius a carries a net positive charge 3Q , uniformly distributed

throughout its volume.Concentric with this sphere is a conducting spherical shell with inner

radius b and outer radius c, and having a net charge 'Q , as shown in Figure. (a) Construct a

spherical gaussian surface of radius r > c and find the net charge enclosed by this surface.

(b) What is the direction of the electric field at r > c? (c) Find the electric field at r > c.

(d) Find the electric field in the region with radius r where c > r > b. (e) Construct a

spherical gaussian surface of radius r, where c > r > b, and find the net charge enclosed by

this surface. (f) Construct a spherical Gaussian surface of radius r, where b > r > a, and find

the net charge enclosed by this surface. (g) Find the electric field in the region b > r > a. (h)

Construct a spherical Gaussian surface of radius r < a, and find an expression for the net

charge enclosed by this surface, as a function of r. Note that the charge inside this surface is

less than 3Q. (i) Find the electric field in the region r < a. ( j) Determine the charge on the

inner surface of the conducting shell. (k) Determine the charge on the outer surface of the

conducting shell. (l) Make a plot of the magnitude of the electric field versus r.

Chapter Practice Problems

FIITJEE CHENNAI CENTRE. 175 Poonamallee High Road. Opp. Ega Theatre, Kilpauk. Chennai-10 Ph: 044 - 42859701

10. .A particle of mass m and charge q moves at high speed along the x axis. It is initially near x = −∞ , and it ends up

near x = +∞ . A second charge Q is fixed at the point x = 0, y = -d. As the moving charge passes the stationary

charge, its x component of velocity does not change appreciably, but it acquires a small velocity in the y direction.

Determine the angle through which the moving charge is deflected. Suggestion: The integral you encounter in

determining yV can be evaluated by applying Gauss’s law to a long cylinder of radius d, centered on the stationary

charge.

11. An infinitely long insulating cylinder of radius R has a volume charge density that varies with the radius as

o

rab

ρ ρ = −

where oρ , a, and b are positive constants and r is the distance from the axis of the cylinder. Use

Gauss’s law to determine the magnitude of the electric field at radial distances. (a) r > R and (b) r < R.

12. Review problem. Four identical particles, each having charge +q, are fixed at

the corners of a square of side L fifth point charge – Q lies a distance z along

the line per pendicular to the plane of the square and passing through the center

of the square (a) show that the force exerted by the other four charges on – Q is

( )3/ 2

2 2

4 ˆ

/ 2

ek qQzF k

z L

= − +

Note that this force is directed toward the center of

the square whether z is positive ( - Q above the square) or negative ( - Q below

the square). (b) If z is small compare with L, the above expression reduces to

( )constantF ≈ − z why does this imply that the motion of the charge – Q simple

harmonic, and what is the period of this motion the mass of – Q is m?

13. A conducting spherical shell of inner radius a and outer radius b carries a net charge Q. A point charge q is placed at

the center of this shell. Determine the surface charge density on (a) the inner surface of the shell and (b) the outer

surface of the shell.

14. A hollow conducting sphere is surrounded by a larger concentric spherical conducting shell. The inner sphere has

charge – Q, and the outer shell has net charge +3Q. The charges are in electrostatic equilibrium. Using Gauss’s law,

find the charges and the electric fields everywhere.

15. A positive point charge is at a distance R/2 from the center of an uncharged thin conducting spherical shell of radius R.

Sketch the electric field lines set up by this arrangement both inside and outside the shell.

16. A long, straight wire is surrounded by a hollow metal cylinder whose axis coincides with that of the wire. The wire

has a charge per unit length of λ , and the cylinder has a net charge per unit length of 2λ . From this information, use Gauss’s law to find (a) the charge per unit length on the inner and outer surfaces of the cylinder and (b) the electric

field outside the cylinder, a distance r from the axis.

17. A nonuniform electric field is given by the expression ˆˆ ˆ ,E ayi bzj cxk= + + where a, b, and c are constants. Determine

the electric flux through a rectangular surface in the xy plane, extending from x = 0 to x = ω and from y = 0 to y = h.

18. A dipole is placed at origin of coordinate system as shown in figure, find the electric field at

point P (0, y).

y

x P 0

45

P