Coulomb's law and negative charges

[bobsmith76]

Homework Statement

see attachment

Homework Equations

The Attempt at a Solution

Do you see the step where they go from (1.35k_eq²)/a²

to 1.91k_eq²)/a² ?

I can't get that step. To my mind. If you square 1.35 then take its square root, you get 1.35 not 1.91

 

[RoshanBBQ]

Homework Statement

see attachment

Homework Equations

The Attempt at a Solution

Do you see the step where they go from (1.35k_eq²)/a²

to 1.91k_eq²)/a² ?

I can't get that step. To my mind. If you square 1.35 then take its square root, you get 1.35 not 1.91

$$\sqrt{1.35^2 \left (\frac{k_e q^2}{a^2} \right )^2 +1.35^2 \left (\frac{k_e q^2}{a^2} \right )^2}$$
$$\sqrt{\left (\frac{k_e q^2}{a^2} \right )^2(1.35^2 +1.35^2) }$$
$$\frac{k_e q^2}{a^2}\sqrt{1.35^2 +1.35^2 }$$
$$\frac{k_e q^2}{a^2}\sqrt{(2)(1.35^2)}$$
$$\frac{k_e q^2}{a^2}\sqrt{2}1.35$$
$$\frac{k_e q^2}{a^2}1.91$$

 

[SammyS]

If you square 1.35 then multiply by 2, then take the square root of that result you do get 1.91, approximately.

 

[bobsmith76]

Roshan,

Excellent answer. If only more math texts included as many steps as you do! I really appreciate it.

 

[asteriatic]

.

Coulomb's law states that the force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This means that as the distance between two charges decreases, the force between them increases, and vice versa.

In the given problem, we are calculating the force between two negative charges using Coulomb's law. It is important to note that the negative sign in front of the charges indicates that they are repelling each other, as like charges repel.

As for the question about the calculation, it seems that there may be a mistake in the given solution. Squaring 1.35 would indeed give 1.8225, not 1.91. This could be a typo or an error in the solution. The correct calculation should be (1.35 ke)(2)/a^2 = 1.8225 ke/a^2. It is important to double check calculations and solutions in scientific work to ensure accuracy.