Two charges 1C and 2C are placed at coordinates (0,3) and (4,3) respectively in an XY plane. What is the work done to put a 30C charge at the origin of the coordinate system?

Step-by-step solution

The potential at the origin due to the charges q₁ and q₂ is given by V = V₁ + V₂ . The distance of the first charge q₁ = 1 C at (0, 3) from the origin is r₁ = 3 m . The distance of the second charge q₂ = 2 C at (4, 3) from the origin is r₂ = 4^2 + 3^2 = 5 m . The total electric potential at the origin is V = 1 4 ₀ ( q₁ r₁ + q₂ r₂ ) . Substituting the given values, we get V = 9 10^9 ( 1 3 + 2 5 ) . V = 9 10^9 ( 5 + 6 15 ) = 9 10^9 ( 11 15 ) = 6.6 10^9 V . The work done to bring a charge q₃ = 30 C to the origin is W