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Please sir reply to this question.Two metal spheres each of radius r and seperated by distance d,have equal and opposite charges.If d>>r the capacitance of the system is(I have doubt C=Q/V,but here qnet=0 as two equal and oopposite charges are present.so the capacitance must be zero.but this is incorrect. why??)

Kaushki

6 Years agoGrade 12th pass

2 Answers

Arun

6 Years ago

Before contact, charges of each spheres,

q

1

=σ4πR

2

;q

2

=σ4π(2R)

2

=4q

1

When the two sphere are brought in contact, their charges are shared till their potentials become equal i.e., V

1

=V

2

∴

4πε

0

R

q

1

′

=

4πε

0

(2R)

q

2

′

∴q

2

′

=2q

1

′

....(i)

As there is no loss of charge in the process

∴q

1

′

+q

2

′

=q

1

+q

2

=q

1

+4q

1

=5q

1

=5(σ4πR

2

)

or q

1

′

+2q

1

′

=5σ4πR

2

(using (i))

q

1

′

=

3

5

σ4πR

2

;q

2

′

=2q

1

′

=

3

10

(σ4πR

2

)

σ

1

=

4πR

2

q

1

′

=

3

5

σ,σ

2

=

4π(2R)

2

q

2

′

=

6

5

σBefore contact, charges of each spheres,

q

1

=σ4πR

2

;q

2

=σ4π(2R)

2

=4q

1

When the two sphere are brought in contact, their charges are shared till their potentials become equal i.e., V

1

=V

2

∴

4πε

0

R

q

1

′

=

4πε

0

(2R)

q

2

′

∴q

2

′

=2q

1

′

....(i)

As there is no loss of charge in the process

∴q

1

′

+q

2

′

=q

1

+q

2

=q

1

+4q

1

=5q

1

=5(σ4πR

2

)

or q

1

′

+2q

1

′

=5σ4πR

2

(using (i))

q

1

′

=

3

5

σ4πR

2

;q

2

′

=2q

1

′

=

3

10

(σ4πR

2

)

σ

1

=

4πR

2

q

1

′

=

3

5

σ,σ

2

=

4π(2R)

2

q

2

′

=

6

5

σ

Vikas TU

6 Years ago

Dear student
The above explanation is not properly explained
Please ignore this
We are sorry for inconvenience.
Good Luck
Cheers

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