CBSE Class 12 · 2013 · ElectrostaticsLong Answer

WhatsApp Email

Using Gauss's 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 the variation of electric field as a function of

r > R

and

r < R

(

r

being the distance from the centre of the shell).

Solution

Take a concentric spherical Gaussian surface of radius

r

.
(i) For

r > R

the enclosed charge is

q

E (4 π r^{2}) = \frac{q}{ε _{0}} \Rightarrow E = \frac{1}{4 π ε _{0}} \frac{q}{r ^{2}}

(ii) For

r < R

the enclosed charge is zero:

E = 0

The field is zero inside, jumps to

\frac{1}{4 π ε _{0}} \frac{q}{R ^{2}}

r = R

, then falls as

1/ r^{2}

outside.

CBSE Class 12 Board · 2013 · Subjective

Practise more: all CBSE board PYQs on Electrostatics →

More board questions on Electrostatics

Assertion (A): Equal amounts of positive and negative charges are distributed uniformly on two halves of a thin circular ring as shown in the figure. The resultant electric field at the centre O of the ring is along OC. Reason (R): It is so because the net potential at O is not z …
CBSE 2024View solution →
Four point charges of $1 μ C$ , $- 2 μ C$ , $1 μ C$ and $- 2 μ C$ are placed at the corners A, B, C and D respectively of a square of side 30 cm. Find the net force acting on a charge of $4 μ C$ placed at the centre of the square.
CBSE 2024View solution →
Three point charges $1 pC$ each are kept at the vertices of an equilateral triangle of side 10 cm. Find the net electric field at the centroid of the triangle.
CBSE 2024View solution →
(a)(i) Draw equipotential surfaces for an electric dipole. (ii) Two point charges $q_{1}$ and $q_{2}$ are located at $r_{1}$ and $r_{2}$ respectively in an external electric field $E$ . Obtain an expression for the potential energy of the system. (iii) The dipole moment …
CBSE 2024View solution →
(b)(i) A thin spherical shell of radius $R$ has a uniform surface charge density $σ$ . Using Gauss's law, deduce an expression for the electric field (i) outside and (ii) inside the shell. (ii) Two long straight thin wires AB and CD have linear charge densities …
CBSE 2024View solution →
The magnitude of the electric field due to a point charge object at a distance of 4.0 m is 9 N/C. From the same charged object the electric field of magnitude 16 N/C will be at a distance of
CBSE 2023View solution →