Two point charges 6mew Coulomb and 2 new coulomb separated by distance 3cm in free space calculate work done in separating them to infinity
To calculate the work done in separating two point charges to infinity, we can use the formula:
Work = Potential Energy(final) - Potential Energy(initial)
The potential energy between two charges in free space is given by:
Potential Energy = (1 / 4πε₀) * (q₁q₂ / r)
Where:
- q₁ and q₂ are the magnitudes of the charges,
- r is the distance between the charges, and
- ε₀ is the permittivity of free space (ε₀ = 8.85 x 10⁻¹² C²/N·m²).
Given:
q₁ = 6 mC
q₂ = 2 nC = 2 x 10⁻⁹ C
r = 3 cm = 3 x 10⁻² m
First, let's calculate the initial potential energy when the charges are at a distance of 3 cm:
Potential Energy(initial) = (1 / 4πε₀) * (q₁q₂ / r)
Substituting the given values:
Potential Energy(initial) = (1 / (4π * (8.85 x 10⁻¹²) C²/N·m²)) * ((6 x 10⁻³ C) * (2 x 10⁻⁹ C) / (3 x 10⁻² m))
Simplifying:
Potential Energy(initial) ≈ 6.77 x 10⁷ N·m
Next, we need to find the potential energy when the charges are separated to infinity. The potential energy at infinity is zero, as the charges are effectively isolated from each other.
Potential Energy(final) = 0
Now, we can calculate the work done:
Work = Potential Energy(final) - Potential Energy(initial)
= 0 - (6.77 x 10⁷ N·m)
= -6.77 x 10⁷ N·m
Therefore, the work done in separating the two charges to infinity is approximately -6.77 x 10⁷ N·m. The negative sign indicates that work is done to move the charges apart.