Advertisements
Advertisements
प्रश्न
Given the electric field in the region `vecE=2xhati`, find the net electric flux through the cube and the charge enclosed by it.
Advertisements
उत्तर
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
संबंधित प्रश्न
Consider two hollow concentric spheres, S1 and S2, enclosing charges 2Q and 4Q respectively as shown in the figure. (i) Find out the ratio of the electric flux through them. (ii) How will the electric flux through the sphere S1 change if a medium of dielectric constant 'εr' is introduced in the space inside S1 in place of air ? Deduce the necessary expression
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?
Define Electric Flux.
It is said that any charge given to a conductor comes to its surface. Should all the protons come to the surface? Should all the electrons come to the surface? Should all the free electrons come to the surface?
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 uniform electric field of intensity 400 N/C, exists in a certain region. How much flux will cross a given area of 10 cm2 in this region, if the area vector is inclined at 60° to the direction of the field?
A charge Qµc is placed at the centre of a cube the flux coming from any surface will be.
An electric charge q is placed at the center of a cube of side ℓ. The electric flux on one of its faces will be ______.
What will be the total flux through the faces of the cube (figure) with side of length a if a charge q is placed at
- A: a corner of the cube.
- B: mid-point of an edge of the cube.
- C: centre of a face of the cube.
- D: mid-point of B and C.
