Question

33. A system consists of two charges 4 uC and 3 uc
with no external field placed at (-5 cm, 0, 0) and
(5 cm, 0, 0) respectively. The amount of work
required to separate the two charges infinitely away
from each other is
​

Answer 1

Given :

The magnitude of charge 1 (q₁) = 4μC

The magnitude of charge 2 (q₂) = 3μC

To Find :

The amount of work required to separate two charges infinitely each other

Solution :

• The distance between the two charges = 5-(-5) = 10cm

• The electrostatic potential of the system =  $k\frac{q_{1} q_{2} }{r}$

         $U_{Initial}= 9\times 10^{9} \times \frac{4\times -3\times 10^{-12}}{10\times 10^{-2}}$

         $U_{initial} = -1.08Joules$

• If the particles are separated infinitely from eatch other the potential between them will become zero  

• Work done to separate the charges = $U_{final}-U_{initial}$

         $W =U_{final}-U_{initial}$

         $W=0-(-1.08)$

         $W=1.08 Joules$

The work done in separating the charges is 1.08J.

Answer 2

The amount of work  required to separate the two charges infinitely away  from each other is 2.16 Joules.

Explanation:

The electrostatic potential is given by the formula:

U = 1/4πε₀ × (q₁q₂)/r

Where,

1/4πε₀ = 7 × 10⁻⁶

q₁ = 4 × 10⁻⁶

q₂ = 3 × 10⁻⁶

r = 5 + 5 = 10 cm

On substituting the values, we get,

U = 9 × 10⁹ × (4 × 10⁻⁶ × -3 × 10⁻⁶)/(10 × 10⁻²)

∴ U = -2.16 J

The work done is given by the formula:

W = Ufinal - Uinitial

On substituting the values, we get,

W = 0 - (-2.16)

∴ W = 2.16 J