Advertisements
Advertisements
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.
उत्तर
(i) At point C, inside the shell
The electric field inside a spherical shell is zero thus, the force experienced by the charge at the centre of the shell C will also be zero.
`.:vec(F_C)=qvecE `
`.:vec(F_C)=0`
At point A,
`|vec(F_A)|=2Q(1/(4piepsilon_0)((3Q)/2)/x^2)`
`vecF_A=(3Q^2)/(4piepsilon_0x^2),`
(ii) Electric flux through the shell
`phi=1/epsilon_0xx" magnitude of the charge enclosed by the shell"`
`phi=1/epsilon_0xxQ/2=Q/(2epsilon_0)`
APPEARS IN
संबंधित प्रश्न
Use Gauss's law to find the electric field due to a uniformly charged infinite plane sheet. What is the direction of field for positive and negative charge densities?
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’ law deduce the expression for the electric field due to a uniformly charged spherical conducting shell of radius R at a point
(i) outside and (ii) inside the shell.
Plot a graph showing variation of electric field as a function of r > R and r < R.
(r being the distance from the centre of the shell)
A charge Q is uniformly distributed on a spherical shell. What is the field at the centre of the shell? If a point charge is brought close to the shell, will the field at the centre change? Does your answer depend on whether the shell is conducting or non-conducting?
Find the flux of the electric field through a spherical surface of radius R due to a charge of 10−7 C at the centre and another equal charge at a point 2R away from the centre in the following figure.
A spherical volume contains a uniformly distributed charge of density 2.0 × 10 -4 Cm-3 Find the electric field at a point inside the volume at a distance 4⋅0 cm from the centre.
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.
“A uniformly charged conducting spherical shell for the points outside the shell behaves as if the entire charge of the shell is concentrated at its centre”. Show this with the help of a proper diagram and verify this statement.
