Question

A charge q produces an electric field of strength 4E at a distance of d away. Determine the electric field strength at a distance of
`(1)/(3)`d away.

a.)
`(1)/(36)`E


b.)
`(1)/(9)`E


c.) 36E


d.) 9E

Answer 1

36E

Step-by-step explanation:

Answer 2

c.) 36E

Step-by-step explanation:

The magnitude of the electric field is given by the expression

`E=k (q)/(d^2)` (1)

where k is the Coulomb's constant, q is the charge that generates the field, and d is the distance from the charge.

In this problem, we have that the magnitude of the field at a distance d is 4E, so we can rewrite the previous equation as

`4E = k(q)/(d^2)`

Now we want to determine the electric field at a distance of
`d'=(1)/(3)d` away. Substituting into (1), we find

`E' = k (q)/(d'^2)=k (q)/(((1)/(3)d)^2)=9 k (q)/(d^2)` (2)

We also know that

`4E = k(q)/(d^2)` (3)

So combining (2) with (3), we find a relationship between the original field and the new field:

`E' = 9 \cdot (4E) = 36E`