Advertisements
Advertisements
Question
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.
Solution
(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
RELATED QUESTIONS
A point object is placed on the principal axis of a convex spherical surface of radius of curvature R, which separates the two media of refractive indices n1 and n2 (n2 > n1). Draw the ray diagram and deduce the relation between the object distance (u), image distance (v) and the radius of curvature (R) for refraction to take place at the convex spherical surface from rarer to denser medium.
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’ 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)
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?
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.
