Question

How will the electrostatic force between two electric charges change if the first charge is doubled and the second charge is only one third of the original charge?

A) 4/9
B) 2/3
C) 6 times
D) 2/9

Answer 1

The new electrostatic force between two electric charges when the first charge is doubled and the second charge is one third of the original charge is 2/3 of the original force. The correct answer is B) 2/3.

Step-by-step explanation:

The electrostatic force between two electric charges can be determined using Coulomb's Law, which states that the force (F) between two charges is directly proportional to the product of the magnitude of the charges (q1 and q2) and inversely proportional to the square of the distance (r) between them. Mathematically, F = k * (q1 * q2) / r^2, where k is Coulomb's constant.

When the first charge is doubled and the second charge becomes one third of its original value, the new force can be calculated as follows.

Original force (F) = k * (q1 * q2) / r^2
New force (F') = k * ((2 * q1) * (q2 / 3)) / r^2
F' = (2/3) * k * (q1 * q2) / r^2
F' = (2/3) * F

Therefore, the new electrostatic force is 2/3 of the original force. The correct answer is B) 2/3.

Answer 2

B)
`(2)/(3)`

Step-by-step explanation:

The electric force between charges can be determined by;

F =
`(kq_(1) q_(2) )/(r^(2) )`

Where: F is the force, k is the Coulomb's constant,
`q_(1)` is the value of the first charge,
`q_(2)` is the value of the second charge, r is the distance between the centers of the charges.

Let the original charge be represented by q, so that;

`q_(1)` = 2q

`q_(2)` =
`(q)/(3)`

So that,

F =
`q_(1)`
`q_(2)` x
`(k)/(r^(2) )`

= 2q x
`(q)/(3)` x
`(k)/(r^(2) )`

=
`(2q^(2) )/(3)` x
`(k)/(r^(2) )`

=
`(2)/(3)` x
`(kq)/(r^(2) )`

F =
`(2)/(3)` x
`(kq)/(r^(2) )`

The electric force between the given charges would change by
`(2)/(3)`.