Advertisements
Advertisements
प्रश्न
A hollow cylindrical box of length 0.5 m 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 `vecE = 20 xhati` where E is NC−1 and x is in metres. Find
(i) Net flux through the cylinder.
(ii) Charge enclosed by the cylinder.
Advertisements
उत्तर
(i) Given,
As the electric field is only along the x-axis, so, flux will pass only through the cross-section of cylinder.
Magnitude of electric field at A,
`E_A = 20 xx 0.5 = 10 N C^-1`
Magnitude of lelectic field at cross - section B
EB = 20 × 1= 20 NC-1
The corresponding eletric fluxes are
`phi_A = vecE.Δvecs = 10 xx 20 xx 10^-4 xx cos 180° = - 0.02 N m^2 C^-1`
`phi_B = vecE.Δvecs = 20 xx 20 xx 10^-4 xx cos0° = 0.04 N m^2 C^-1`
So, the net flux through the cylinder,
`phi = phi _A + phi_B = - 0.02 + 0.04 = 0.02 N m^2 C^-1 xx 10^12C`
(ii) Using Gauss’s law:
`oint vecE. vecds = q/in_0 => 0.02 = q/(8.85 xx 10^-12) => q =8.85 xx 0.02 xx 10^-12 = 0.177 xx 10^12 C`
APPEARS IN
संबंधित प्रश्न
Electric potential decreases uniformly from 120 V to 80 V, as one moves on the x-axis from x = −1 cm to x = +1 cm. The electric field at the origin
(a) must be equal to 20 Vcm−1
(b) may be equal to 20 Vcm−1
(c) may be greater than 20 Vcm−1
(d) may be less than 20 Vcm−1
The electric field in a region is directed outward and is proportional to the distance rfrom the origin. Taking the electric potential at the origin to be zero,
A wire is bent in the form of a regular hexagon and a total charge q is distributed uniformly on it. What is the electric field at the centre? You may answer this part without making any numerical calculations.
A ball of mass 100 g and with a charge of 4.9 × 10−5 C is released from rest in a region where a horizontal electric field of 2.0 × 104 N C−1 exists. (a) Find the resultant force acting on the ball. (b) What will be the path of the ball? (c) Where will the ball be at the end of 2 s?
A block of mass m with a charge q is placed on a smooth horizontal table and is connected to a wall through an unstressed spring of spring constant k, as shown in the figure. A horizontal electric field E, parallel to the spring, is switched on. Find the amplitude of the resulting SHM of the block. 
12 J of work has to be done against an existing electric field to take a charge of 0.01 C from A to B. How much is the potential difference VB − VA?
Which of the following methods can be used to charge a metal sphere positively without touching it? Select the most appropriate.
The surface charge density of a thin charged disc of radius R is σ. The value of the electric field at the center of the disc is `sigma/(2∈_0)`. With respect to the field at the center, the electric field along the axis at a distance R from the center of the disc ______.
Five charges, q each are placed at the corners of a regular pentagon of side ‘a’ (Figure).
(a) (i) What will be the electric field at O, the centre of the pentagon?
(ii) What will be the electric field at O if the charge from one of the corners (say A) is removed?
(iii) What will be the electric field at O if the charge q at A is replaced by –q?
(b) How would your answer to (a) be affected if pentagon is replaced by n-sided regular polygon with charge q at each of its corners?
