The electric field of a charge Q at a distance d away is measured as E What will the electric field measure at a distance 1/2 d away from the charge?

Correct answer: E₁ = 4 · E The electric field increased four times

Explanation:

Given:

E - Electric field at distance d

E₁ - Electric field at distance d₁

Q - Charge of an object

d₁ = (1/2) d

The formula by which the electric field is calculated is:

E = k Q / d²

Electric field at a distance d₁

E₁ = k Q / d₁²

We will form their quotient

E₁ / E = ((k Q) / d₁²) / ((k Q) / d²)

When the constant k and the charge Q is canceled we get:

E₁ / E = (1 / d₁²) / (1 / d²) = d² / d₁² = d² / ((1/2) d) ² = 1 / (1/4) = 4

E₁ = 4 · E

The electric field increased four times

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