Advertisements
Advertisements
Question
A thin straight infinitely long conducting wire having charge density λ is enclosed by a cylindrical surface of radius r and length l, its axis coinciding with the length of the wire. Find the expression for the electric flux through the surface of the cylinder.
Advertisements
Solution
The thin infinitely long straight line has a linear charge density λ.
Since the electric field for this kind of configuration will be radial and perpendicular to the wire, there will be no flux through the flat surfaces of the cylinder. Also, the electric field (E) will be constant at every point on the curved surface of the cylinder (as all points on it are equidistant from the wire) and perpendicular to it.
We shall us Gauss's law to find the electric flux through the cylinder. The charge enclosed by the cylinder is λ × l, as l is the length of the cylinder and it is also the length of the charged wire within the cylinder.
We know,
`\text { Electric flux} = (\text { Charge enclosed})/epsi_0 = (lambdal)/epsi_0`
APPEARS IN
RELATED QUESTIONS
Write S.I unit of electric flux.
Given a uniform electric field `vecE=5xx10^3hati`N/C, find the flux of this field through a square of 10 cm on a side whose plane is parallel to the y-z plane. What would be the flux through the same square if the plane makes a 30° angle with the x-axis ?
Given a uniform electric filed \[\vec{E} = 4 \times {10}^3 \ \hat{i} N/C\]. Find the flux of this field through a square of 5 cm on a side whose plane is parallel to the Y-Z plane. What would be the flux through the same square if the plane makes a 30° angle with the x-axis?
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’?
A small plane area is rotated in an electric field. In which orientation of the area, is the flux of the electric field through the area maximum? In which orientation is it zero?
If the flux associated with a coil changes at the rate of 360 webers every 4 minutes, then the induced e.m.f. is ______
A charge 'Q' µC is placed at the centre of a cube. The flux through one face and two opposite faces of the cube is respectively ______.
The total flux through the faces of the cube with side of length a if a charge q is placed at corner A of the cube is ______.
A point charge q is placed at a distance a/2 directly above the centre of a square of side a. The electric flux through the square is ______.
The S.I. unit of electric flux is ______
