Home
Class 12
PHYSICS
Answer the following: (a) State Gauss'...

Answer the following:
(a) State Gauss' law. Using this law, obtain the expression for the electric field due to an infinitely long straight conductor of linear charge density `lamda`.
(b) A wire AB of length L has linear charge density `lamda = kx`, where x is measured from the end A of the wire.
This wire is enclosed by a Gaussian hollow surface. Find the expression for the electric flux through this surface.

Text Solution

Verified by Experts

(a) Gauss's Law
(b) length = L
`lamda = kx`
`:. lamda = (Q)/(L)`
charge on elementary length 'dx' at a distance x from end A is
`kx = (Q)/(L) " " dq = lamda dx`
`rArr Q = kxL " " dq = kxdx`
Now, `q = (kx L)/(epsi_(0)) " " :.` total charge on the road = `int dr = underset(0)overset(L)int kxdx`
`Q = (kxL)/(epsi_(0)) " " q = (kL^(2))/(2)`
`:.` flux emitted by the charged rod and passing through the Gaussian surface.
`psi = (q)/(in_(0)) " " |psi = (KL^(2))/(2 in_(0))|`
Promotional Banner

Similar Questions

Explore conceptually related problems

Answer the following: State Gauss' law in electrostatics. Derive an expression for the electric field due to an infinitely long straight uniformly charged wire.

State Gauss's law in electrostatics. Use this law to derive an expression for the electric field due to an infinitely long straight wire of linear charge density lamda cm^(-1)

Using Gauss’ law, derive an expression for the electric field at a point near an infinitely long straight uniformly charged wire.

State Gauss's law in electrostatics. Using this law derive an expression for the electric field due to a uniformly charged infinite plane sheet.

Electric field due to an infinite non-conducting sheet of surface charge density sigma , at a distance r from it is

The electric field at distance .r. from infinte line of charge ("having linear charge density" lambda) is

If linear charge density of a wire as shown in the figure is lambda

Find the electric field due to an infinitely long cylindrical charge distribution of radius R and having linear charge density lambda at a distance half of the radius from its axis.

What is the electric field intensity at any point on the axis of a charged rod of length 'L' and linear charge density lambda ? The point is separated from the nearer end by a.

Find the electric field at point O, due to the segment of a ring, whose linear charge density is 8 C //cm