Advertisements
Advertisements
प्रश्न
Find the electric field intensity due to a uniformly charged spherical shell at a point (ii) inside the shell. Plot the graph of electric field with distance from the centre of the shell.
उत्तर
Field inside the shell: The point P will be inside the shell. The Gaussian surface is again a sphere through P centred at O.
The flux through the Gaussian surface, calculated as before, is E × 4πr2.
However, in this case, the Gaussian surface encloses no charge. Gauss’s law then gives
E = 4πr2 = 0
∴ E = 0
Thus, the field due to a uniformly charged thin shell is zero at all points inside the shell
Graph showing the electric field with the distance from the centre of the shell:
APPEARS IN
संबंधित प्रश्न
A thin metallic spherical shell of radius R carries a charge Q on its surface. A point charge`Q/2` is placed at its centre C and an other charge +2Q is placed outside the shell at a distance x from the centre as shown in the figure. Find (i) the force on the charge at the centre of shell and at the point A, (ii) the electric flux through the shell.
Two large, thin metal plates are parallel and close to each other. On their inner faces, the plates have surface charge densities of opposite signs and of magnitude 17.0 × 10−22 C/m2. What is E:
- in the outer region of the first plate,
- in the outer region of the second plate, and
- between the plates?
Using Gauss's law in electrostatics, deduce an expression for electric field intensity due to a uniformly charged infinite plane sheet. If another identical sheet is placed parallel to it, show that there is no electric field in the region between the two sheets ?
A small conducting sphere of radius 'r' carrying a charge +q is surrounded by a large concentric conducting shell of radius Ron which a charge +Q is placed. Using Gauss's law, derive the expressions for the electric field at a point 'x'
(i) between the sphere and the shell (r < x < R),
(ii) outside the spherical shell.
Using Gauss’s law, prove that the electric field at a point due to a uniformly charged infinite plane sheet is independent of the distance from it.
How is the field directed if (i) the sheet is positively charged, (ii) negatively charged?
A spherical shell made of plastic, contains a charge Q distributed uniformly over its surface. What is the electric field inside the shell? If the shell is hammered to deshape it, without altering the charge, will the field inside be changed? What happens if the shell is made of a metal?
A rubber balloon is given a charge Q distributed uniformly over its surface. Is the field inside the balloon zero everywhere if the balloon does not have a spherical surface?
A large non-conducting sheet M is given a uniform charge density. Two uncharged small metal rods A and B are placed near the sheet as shown in the following figure.
(a) M attracts A.
(b) M attracts B.
(c) A attracts B.
(d) B attracts A.
A circular wire-loop of radius a carries a total charge Q distributed uniformly over its length. A small length dL of the wire is cut off. Find the electric field at the centre due to the remaining wire.