Question

A point charge with a charge q1 = 3.60 μC is held stationary at the origin. A second point charge with a charge q2 = -4.60 μC moves from the point x= 0.100 m , y= 0 to the point x= 0.250 m , y= 0.250 m .How much work W is done by the electric force on the moving point charge?

Answer 1

The work W that is done by the electric force in the moving point charge is; 1.022 J

Work done on a moving charge

We are given;

• Charge 1; q₁ = 3,60 μC = 3.6 × 10⁻⁶ C

• Charge 2; q₂ = -4.40 μC = -4.4 × 10⁻⁶ C

We are told that the first charge is held stationary at the origin. Thus;

r₁ = √(0.100² + 0²)

r₁ = 0.1 m

Similarly distance of second charge is;

r₂ = √(0.250² + 0.250²)

r₂ = √0.125

r₂ = 0.354 m

Formula for work done on the moving point charge is;

W = U₁ - U₂

W = [(k * |q₁| * |q₂|)/r₁] - [(k * |q₁| * |q₂|)/r₂]

We are taking absolute value of the charges and so none of the charges will be negative

This can be further simplified as;

W = (k * |q₁| * |q₂|) * (1/r₁ - 1//r₂)

Plugging in the relevant values gives us;

W = (8.99 × 10⁹ × 3.6 × 10⁻⁶ × 4.4 × 10⁻⁶) × (¹/₀.₁ - ¹/₀.₃₅₄)

W = 1.022 J

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