An isolated charged point particle produces an electric field with magnitude E at a point 2 m away. At a point 1 m from the particle the magnitude of the field is:]

At a point 1 m from the particle, the magnitude of the electric field is;

4 times the magnitude of the electric field is at a distance of 2 m from the particle.

Formula for magnitude of electric field is;

E = kq/r²

where;

k is a constant = 8.99 x 10⁹ N.m²/C²

r is distance from the charged particle

q is the charge

Now, when r = 2, we have;

E₁ = kq/2²

E₁ = kq/4   ---(eq 1)

Now, when r = 1, we have;

E₂ = kq/1²

E₂ = kq  ---(eq 2)

Let us now divide eq 2 by eq 1 to get;

E₂/E₁ = kq/(kq/4)

E₂/E₁ = 4

E₂ = 4E₁

Thus, at a point 1 m from the particle, the magnitude of the electric field is 4 times the magnitude of the electric field is at a distance of 2 m from the particle.

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Explanation:

The electric field at a distance r from the charged particle is given by :

k is electrostatic constant

if r = 2 m, electric field is given by :

If r = 1 m, electric field is given by :

Dividing equation (1) and (2) we get :

So, at a point 1 m from the particle, the electric field is 4 times of the electric field at a point 2 m.