Advertisements
Advertisements
Question
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
Advertisements
Solution
(i) Charge enclosed by sphere S1 = 2Q
By Gauss law, electric flux through sphere S1 is
`phi_1=(2Q)/in_0`
Charge enclosed by sphere S2 = 2Q+4Q=6Q
`:.phi_2=(6Q)/in_0`
The ratio of the electric flux is
`phi_1/phi_2=((2Q)/in_0)/((6Q)/in_0)=2/6=1/3`
(ii) For sphere S1, the electric flux is
`phi'=(2q)/in_r`
`:.(phi')/phi_1=in_0/in_r`
`=>phi'=phi_1.in_0/in_r`
∵ εr > ε0
`:.phi'
Therefore, the electric flux through the sphere S1 decreases with the introduction of the dielectric inside it.
APPEARS IN
RELATED QUESTIONS
What is the net flux of the uniform electric field of previous question through a cube of side 20 cm oriented so that its faces are parallel to the coordinate planes?
A charge q is placed at the centre of the open end of a cylindrical vessel (see the figure). The flux of the electric field through the surface of the vessel is ____________ .
Mark the correct options:
The following figure shows a closed surface that intersects a conducting sphere. If a positive charge is placed at point P, the flux of the electric field through the closed surface
The electric field in a region is given by `vec"E"` = 5 `hatk`N/C. Calculate the electric flux Through a square of side 10.0 cm in the following cases
- The square is along the XY plane
- The square is along XZ plane
- The normal to the square makes an angle of 45° with the Z axis.
The electric flux through the surface ______.
 |
 |
 |
 |
| (i) | (ii) | (iii) | (iv) |
In a region of space having a uniform electric field E, a hemispherical bowl of radius r is placed. The electric flux Φ through the bowl is:
A charge Qµc is placed at the centre of a cube the flux coming from any surface 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?
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 charge q is replaced by an electric dipole?
