**What is the angle? (two point charges on 1.0m long threads repel each other after being charged…**

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## Question “What is the angle? (two point charges on 1.0m long threads repel each other after being charged…”

Two 5.0g point charges on 1.0m long threads repel each other after being charged to +100 nC, as shown in the figure.

What is the angle theta?You can assume that theta is a small angle.

The answer is 4.4 degree.Please give steps to getting the answer.

## Answer

Trigonometric relations, force equilibrium and electrostatic force are all concepts that can be used to solve this problem.

First, think about the components of tension in the thread. To simplify the tension equation, you can use trigonometric relationships later. To calculate the angle, you can compare the force component to other equivalent forces.

Two components make up the tension of a thread that holds a mass at an angle to its vertical axis. The horizontal component of tension is.

here is tension. angle is from vertical axis.

The vertical component is the tension.

The object’s weight is.

here is the object’s mass and the acceleration caused by gravity.

The electrostatic force between identical charges is called,

The Coulomb constant is the charge for each charged particle. It is also the distance between them.

, and MediaTag13 .

The opposite side is the angle in a right triangle.

refers to the length of hypotenuse.

Two components of force are present in the tension that holds two charged particles to the thread.

The horizontal component is called tension.

The electrostatic force between the charges is equal to its horizontal component. The electrostatic force between charges is.

The distance between charges is

Substitute HTMLMediaTag19 for HTMLMediaTag20 within the expression of electrostatic force . The electrostatic force between two point charges is:

The horizontal component of thread tension is

Substitute HTMLMediaTag24 for or to .

The angle that charges make with the vertical axis of the earth is very small. Therefore,

Substitute HTMLMediaTag30 for The horizontal component of tension is on the thread.

The vertical component is tension.

The weight of the charged particle is what balances the vertical component of tension on the thread. The charged particle’s weight is.

The vertical component is tension.

Substitute HTMLMediaTag36 to

or MediaTag38 to . The vertical component of force can be described as:

The angle that charges make with the vertical axis of the earth is very small. Therefore,

Substitute HTMLMediaTag42 with HTMLMediaTag43 The tension on the thread’s vertical component is,

The charges have a vertical component that causes tension to be applied to the thread.

The charges have a horizontal component that causes tension to be applied to the thread.

To calculate the angle, rewrite the equation for the horizontal component of force. The angle is:

The tension’s vertical component is worth considering. To find the angle, substitute

. The angle is:

Substitute

for

.

for

.

for

.

for

. And

for

.

.

Ans:

The angle HTMLMediaTag63 equals .

## Conclusion

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