Do You Know the Surface Density Ratio of Two Charged Spherical Conductors?

By Team Aakash Byju's | 25th October 2022

Choose the right answer from the options given below

A. If

R

1

,

σ

1

2

2

and

R

σ

,

are the radii and

surface density of spherical conductor 1 and 2 respectively, then

R

,

σ

1

2

2

and

R

σ

,

are the radii and

surface density of spherical conductor 1 and 2 respectively, then

B. If

1

=

σ

1

σ

2

R

2

R

1

=

σ

1

σ

2

2

R

1

R

R

,

σ

1

2

2

and

R

,

are the radii and

surface density of spherical conductor 1 and 2 respectively, then

C. If

1

σ

=

σ

1

σ

2

2

R

1

R

2

R

,

σ

1

2

2

and

R

,

are the radii and

surface density of spherical conductor 1 and 2 respectively, then

D. If

1

σ

=

σ

1

σ

2

2

R

1

R

2

If R1, σ1 and R2, σ2 are the radii and surface density of spherical conductor 1 and 2 respectively, then the correct answer is option A

Arrow

Detailed Explanation

=

σ

1

σ

2

2

R

1

R

If two conductors are connected by a wire, they will have the same potential, i.e., V1 = V2, where V1 is the potential of conductor 1 and V2 is the potential of conductor 2.

Since ,

KQ

1

KQ

2

=

R

1

R

2

=>

Q

1

1

Q

2

=

R

R

2

V = K

Q

R

(

(

We can write

Q1 and Q2 are the charge quantities on each conductor and the charge quantity is Q = σ A (σ is the surface charge density and A is the area of the conductor.)

Therefore,

=>

Q

1

Q

2

=

σ

1

A

4π(R )

1

σ

A

2

2

A

1

=

1

2

A

2

=

4π(R  )

2

2

and

Hence,

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