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
If a body is charged by rubbing it, its weight
A 10-cm long rod carries a charge of +50 μC distributed uniformly along its length. Find the magnitude of the electric field at a point 10 cm from both ends of the rod.
Consider a uniformly charged ring of radius R. Find the point on the axis where the electric field is maximum.
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 particle of mass m and charge q is thrown at a speed u against a uniform electric field E. How much distance will it travel before coming to momentary rest ?
A particle of mass 1 g and charge 2.5 × 10−4 C is released from rest in an electric field of 1.2 × 10 4 N C−1. How long will it take for the particle to travel a distance of 40 cm?
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. 
Consider the situation of the previous problem. A charge of −2.0 × 10−4 C is moved from point A to point B. Find the change in electrical potential energy UB − UA for the cases (a), (b) and (c).
The Electric field at a point is ______.
- always continuous.
- continuous if there is no charge at that point.
- discontinuous only if there is a negative charge at that point.
- discontinuous if there is a charge at that point.
