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Physics Part-I

Electrostatic Potential and Capacitance

A spherical conducting shell of inner radius r_1 and outer rad

Physics Part-I

Class 12

NCERT

Chapter 1: Electric Charges and Fields

47 questions

Chapter 2: Electrostatic Potential and Capacitance

46 questions

Two tiny spheres carrying charges

1.5 μ C

and

2.5 μ C

are located 30 cm apart. Find the potential and electric field:

(a) at the mid-point of the line joining the two charges, and

(b) at a point 10 cm from this midpoint in a plane normal to the line and passing through the mid-point.

A spherical conducting shell of inner radius

r_{1}

and outer radius

r_{2}

has a charge Q.

(a) A charge q is placed at the centre of the shell. What is the surface charge density on the inner and outer surfaces of the shell?

(b) Is the electric field inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape? Explain.

(a) Show that the normal component of electrostatic field has a discontinuity from one side of a charged surface to another given by

(E_{2} - E_{1}) ˙ \overset{n}{^} \frac{σ}{ε _{0}}

where

\overset{n}{^}

is a unit vector normal to the surface at a point and

σ

is the surface charge density at that point. (The direction of

\overset{n}{^}

is from side 1 to side 2.) Hence show that just outside a conductor, the electric field is

σ \overset{n}{^} / ϵ_{0}

(b) Show that the tangential component of electrostatic field is continuous from one side of a charged surface to another. [Hint: For (a), use Gauss's law. For, (b) use the fact that work done by electrostatic field on a closed loop is zero.]

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Chapter 3: Current Electricity

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Chapter 8: Electromagnetic Waves

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Question

Medium

Solving time: 4 mins

A spherical conducting shell of inner radius $r_{1}$ and outer radius $r_{2}$ has a charge Q.
(a) A charge q is placed at the centre of the shell. What is the surface charge density on the inner and outer surfaces of the shell?
(b) Is the electric field inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape? Explain.

Views: 6,652 students

Updated on: Mar 31, 2023

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Physics Part-I (NCERT)

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Jack Discussed

A spherical conducting shell of inner radius

r_{1}

and outer radius

r_{2}

has a charge Q.

(a) A charge q is placed at the centre of the shell. What is the surface charge density on the inner and outer surfaces of the shell?

(b) Is the electric field inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape? Explain.

7 mins ago

Discuss this question LIVE

7 mins ago

Text solutionVerified

(a) The charge of magnitude $+ q$ present inside the spherical shell induces a charge of magnitude $- q$ 0n the inner part of the shell. Therefore, for the charge on the inner part, the surface charge density will be due to $- q$ .

It is given by:

$σ_{1} = \frac{T o t a l c ha r g e}{s u r f a ce a re a o f inn er p a r t}$

$\Rightarrow \frac{- q}{4 π r _{1}^{2}}$

The charge on the outer shell will be $+ q$ and the surface charge density at the outer part will be due to sum of $q$ and $Q$ charges present on the outer shell.

$σ_{2} = \frac{T o t a l c ha r g e}{O u t er s u r f a ce a re a} = \frac{Q + q}{4 π r _{2}^{2}}$ ...(ii)

(b) If we consider a loop inside an irregular conductor, then will be no work done on it as there is no field present inside the cavity. So, there will be no field inside the cavity even if it is irregular in shape.

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Practice more questions from Physics Part-I (NCERT)

Two tiny spheres carrying charges

1.5 μ C

and

2.5 μ C

are located 30 cm apart. Find the potential and electric field:

(a) at the mid-point of the line joining the two charges, and

(b) at a point 10 cm from this midpoint in a plane normal to the line and passing through the mid-point.

A spherical conducting shell of inner radius

r_{1}

and outer radius

r_{2}

has a charge Q.

(a) A charge q is placed at the centre of the shell. What is the surface charge density on the inner and outer surfaces of the shell?

(b) Is the electric field inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape? Explain.

(a) Show that the normal component of electrostatic field has a discontinuity from one side of a charged surface to another given by

(E_{2} - E_{1}) ˙ \overset{n}{^} \frac{σ}{ε _{0}}

where

\overset{n}{^}

is a unit vector normal to the surface at a point and

σ

is the surface charge density at that point. (The direction of

\overset{n}{^}

is from side 1 to side 2.) Hence show that just outside a conductor, the electric field is

σ \overset{n}{^} / ϵ_{0}

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Question Text	A spherical conducting shell of inner radius $r_{1}$ and outer radius $r_{2}$ has a charge Q. (a) A charge q is placed at the centre of the shell. What is the surface charge density on the inner and outer surfaces of the shell? (b) Is the electric field inside a cavity (with no charge) zero, even if the shell is not spherical, but has any irregular shape? Explain.
Updated On	Mar 31, 2023
Topic	Electrostatic Potential and Capacitance
Subject	Physics
Class	Class 12
Answer Type	Text solution:1 Video solution: 3
Upvotes	341
Avg. Video Duration	4 min

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