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.
Advertisements
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
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?
Find the ratio of the potential differences that must be applied across the parallel and series combination of two capacitors C1 and C2 with their capacitances in the ratio 1 : 2 so that the energy stored in the two cases becomes the same.
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.
How is the field directed if (i) the sheet is positively charged, (ii) negatively charged?
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?
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 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 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.
