(i)

(ii) = 12 µC, = 18 µC

(iii)

(iv) 2πε 0 = 3/2 Joules

Sol.

As shown, 10 µC and 20 µC are charge on two spheres before connecting with conducting wire.

Let after connecting with conducting wire, the charges on two spheres ⇒ Q 1 ' & Q 2 '

(i) After connection

Potentials of both spheres are equal

∴ V 1 = V 2

or = 3 Q 1 ' = 2Q 2 '

=

(ii) = (i) & Q 1 '+ Q 2 '(ii) = 30 µC → charge conservation

∴ from (i) & (ii)

Q 2 ' + = 30

or = 30

or Q 2' = µc = 18 µc

& Q 1' = Q 2' = × 18 µc = 12 µc

(iii) = = ×

= × =

(iv) Heat produced during the process ⇒

initial energy of system – final energy of system

⇒ Ui – Uf

⇒ –

Where; C 1 = 4 π∈ 0 r 1

C 2 = 4 π∈ 0 r 2

V 1 = ; V 2 = & V = ; C eq = (C 1 + C 2 )

∴ Heat ⇒ – (C 1 + C 2 )

⇒ –

⇒

⇒ = 2 π∈ 0 (V 1 –V 2 ) 2

∴ Heat = 2 π∈ 0 (V 1 –V2) 2 ⇒ ×

× 10–2 × 9 × 109 = × 107 = × ×10–1

= Joules