Respuesta :

distance is 1/3 of the original, force is 9x the original force.

Answer:

Electric field strength is 4E/9

Explanation:

It is given that, a charge q produces an electric field of strength 4E at a distance of d away.  

The electric field at a distance d is given by :

[tex]E=k\dfrac{q}{d^2}[/tex]......(1)

According to question, [tex]4E=k\dfrac{q}{d^2}[/tex]........(2)

From equation (1), it is clear that electric field strength is inversely proportional to the square of distance between them.

We have to find the electric field strength (E') at a distance of 1/3d away. So,

[tex]E'=k\dfrac{q}{(d/3)^2}[/tex]............(3)

Taking ratios of equation (2) and (3). So,

[tex]\dfrac{4E}{E'}=\dfrac{k\dfrac{q}{d^2}}{k\dfrac{q}{(d/3)^2}}[/tex]

[tex]\dfrac{4E}{E'}=9[/tex]

[tex]E'=\dfrac{4E}{9}[/tex]

So, the electric field strength at a distance of (1/3)d away is 4E/9