Question 786: Electrostats & Capacitance

Question

A conducting sphere of radius ' R ' is given a charge ' $Q$ ' uniformly. The electric field and the electric potential at the centre of the sphere are respectively [ $\varepsilon_0=$ permittivity of free space]

Accepted Answer

Let us solve this step by step using NCERT method:
1. Electric Field at the Centre of a Conducting Sphere
For a
conducting sphere
, the
electric field inside
(including at the centre) is
zero
. This is because charges reside only on the surface and inside the conductor the electric field is always zero (as per electrostatics in conductors).
So,
$$ E_{	ext{centre}} = 0 $$
2. Electric Potential at the Centre
The
electric potential
at any point
inside
a uniformly charged conducting sphere (including its centre) is
equal to the potential at the surface
.
Potential at the surface is given by:
$$ V = \frac{Q}{4\pi\varepsilon_0 R} $$
This same value is also at the centre.
3. Final Answer
So,
electric field at the centre = 0
Potential at the centre = $\dfrac{Q}{4\pi\varepsilon_0 R}$
4. Option Matching
This matches with
Option A
.
Final Answer:
Option A:
zero and $\frac{Q}{4\pi \varepsilon_0 R}$

Answer

zero and $\frac{Q}{4 \pi \varepsilon_0 R}$

Answer

$\frac{\mathrm{Q}}{4 \pi \varepsilon_0 \mathrm{R}^2}$ and zero

Answer

$\frac{\mathrm{Q}}{4 \pi \varepsilon_0 \mathrm{R}}$ and $\frac{\mathrm{Q}}{4 \pi \varepsilon_0 \mathrm{R}^2}$

Answer

zero and zero

Electrostats & Capacitance

A conducting sphere of radius ' R ' is given a charge ' Q ' uniformly. The electric field and the electric potential at the centre of the sphere are respectively [ \varepsilon_0= permittivity of free space]

Choose the correct answer: