# A Spherical Conductor of Radius 12 cm Has a Charge of 1.6 × 10^−7c Distributed Uniformly on Its Surface. What is the Electric Field - Physics

Numerical

A spherical conductor of radius 12 cm has a charge of 1.6 × 10−7C distributed uniformly on its surface. What is the electric field

(a) Inside the sphere

(b) Just outside the sphere

(c) At a point 18 cm from the centre of the sphere?

#### Solution

(a) Radius of the spherical conductor, r = 12 cm = 0.12 m

Charge is uniformly distributed over the conductor, q = 1.6 × 10−7 C

Electric field inside a spherical conductor is zero. This is because if there is a field inside the conductor, then charges will move to neutralize it.

(b) Electric field E just outside the conductor is given by the relation,

"E" = "q"/(4piin_0"r"^2)

Where,

in_0 = Permittivity of free space

1/(4piin_0) = 9 xx 10^9 "N m"^2  "C" ^-2

∴ "E" = (1.6 xx 10^-7 xx 9 xx 10^-9)/(0.12)^2

= 10^5  "N C"^-1

Therefore, the electric field just outside the sphere is 10^5  "N C"^-1.

(c) Electric field at a point 18 m from the centre of the sphere = E1

Distance of the point from the centre, d = 18 cm = 0.18 m

"E"_1 = "q"/(4piin_0"d"^2)

= (9 xx 10^9 xx 1.6 xx 10^-7)/(18 xx 10^-2)^2

= 4.4 xx 10^4 "N"/"C"

Therefore, the electric field at a point 18 cm from the centre of the sphere is 4.4 xx 10^4 "N"/"C".

Concept: Potential Energy in an External Field - Potential Energy of a Single Charge
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#### APPEARS IN

NCERT Physics Part 1 and 2 Class 12
Chapter 2 Electrostatic Potential and Capacitance
Exercise | Q 2.4 | Page 86
NCERT Class 12 Physics Textbook
Chapter 2 Electrostatic Potential and Capacitance
Exercise | Q 4 | Page 87
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