Advertisements
Advertisements
Question
Given the electric field in the region `vecE=2xhati`, find the net electric flux through the cube and the charge enclosed by it.
Solution
Since the electric field has only x component, for faces normal to x direction, the angle between E and ∆S is ±π/2. Therefore, the flux is separately zero for each face of the cube except the two shaded ones.
The magnitude of the electric field at the left face is EL = 0 (As x = 0 at the left face)
The magnitude of the electric field at the right face is ER = 2a (As x = a at the right face)
The corresponding fluxes are
`phi_L=vecE.DeltavecS=0`
`phi_R=vecE_R.DeltavecS=E_RDeltaScostheta=E_RDeltaS " "(.:theta=0^@)`
⇒ϕR= ERa2
Net flux (ϕ) through the cube = ϕL+ϕR=0+ERa2=ERa2
ϕ=2a(a)2=2a3
We can use Gauss’s law to find the total charge q inside the cube.
`phi=q/(epsilon_0)`
q=ϕε0=2a3ε0
APPEARS IN
RELATED QUESTIONS
Define electric flux.
Write its (electric flux.) S.I unit.
Find out the outward flux to a point charge +q placed at the centre of a cube of side ‘a’. Why is it found to be independent of the size and shape of the surface enclosing it? Explain.
A uniformly charged conducting sphere of 2.4 m diameter has a surface charge density of 80.0 μC/m2.
- Find the charge on the sphere.
- What is the total electric flux leaving the surface of the sphere?
Following Figure (a) shows an imaginary cube of edge L/2. A uniformly charged rod of length (L) moves towards the left at a small but constant speed `nu.` At t = 0, the left end just touches the centre of the face of the cube opposite it. Which of the graphs shown in the figure (b) represents the flux of the electric field through the cube as the rod goes through it?
If the flux associated with a coil changes at the rate of 360 webers every 4 minutes, then the induced e.m.f. is ______
An electric charge q is placed at the centre of a cube of side a. The electric flux on one of its faces will be ______.
The S.I. unit of electric flux is ______
The electric charges are distributed in a small volume. The flux of the electric field through a spherical surface of radius 10 cm surrounding the total charge is 20 V-m. The flux over a concentric sphere of radius 20 cm will be ______.
A hollow sphere of radius R has a point charge q at its centre. Electric flux emanating from the sphere is X. How will the electric flux change, if at all, when radius of the sphere is doubled?
