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the electric field due to a point charge q at the point of distance d is E.Where should this point be kept from the same charge so that the electric field at this point becomes E/4​



Answer :

Answer:

The point should be kept 2d from the same charge.

Explanation:

We can find the point from the same charge by using the electric field formula:

[tex]\boxed{E=\frac{kq}{d^2} }[/tex]

where:

  • E = electric field
  • k = electrostatic constant (9 × 10⁹ Nm²/C²)
  • q = electrical charge
  • d = distance

Given:

  • E₁ = E
  • q₁ = q
  • d₁ = d
  • E₂ = E/4
  • q₂ = q

[tex]\displaystyle E_1:E_2=\frac{kq_1}{d_1^2} :\frac{kq_2}{d_2^2}[/tex]

 [tex]\displaystyle E:\frac{E}{4} =\frac{kq}{d^2} :\frac{kq}{d_2^2}[/tex]

    [tex]\displaystyle 1:\frac{1}{4} =\frac{1}{d^2} :\frac{1}{d_2^2}[/tex]

     [tex]4:1=d_2^2:d^2[/tex]

        [tex]d_2^2=4d^2[/tex]

        [tex]d_2=\sqrt{4d^2}[/tex]

        [tex]\bf d_2=2d[/tex]

Therefore, the distance should be 2d.

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