# Finding the angle from two charges repelling each other.

• jheld
In summary, the problem involves two 5.0 g spheres, charged to +91 nC, suspended from 1.0-m-long threads. The spheres repel each other due to their charges and the resulting forces must be in equilibrium. To solve for the unknown angle θ, we must consider the electric force, tension force, and weight acting on the spheres. By drawing a free body diagram and applying the appropriate equations, we can determine the angle θ to be 4.1 degrees.
jheld

## Homework Statement

The figure shows two 5.0 g spheres suspended from 1.0-m-long threads. The spheres repel each other after being charged to +91 nC. What is the angle θ ?

## Homework Equations

I was thinking momentum and/or kinetic energy equations.
k = 1/2 mv^2
p = mv
F = ma

## The Attempt at a Solution

Where's the figure?

Sorry. I just attached it to a file here, so maybe you can see it now.

#### Attachments

• angle between two charges.doc
30.5 KB · Views: 406
What forces are acting on the spheres? Which direction must the resultant force on each sphere point in equilibrium?

Well, there is the electric force. F = qE = Kq_1q_2/r^2.
In equilibrium, they must be pointing in opposite directions, right?

So there is the electric force and the tension force. So Ftotal = T plus qE, right?
I am unsure of how to calculate the tension with no velocity. So, still a little confused.

There's also the gravitational force, i.e. the weight. Draw a free body diagram with all of these forces with their proper directions. The tension points along the string inward. That means that the sum of the weight and the electrostatic force must point along the string but outward in equilibrium.

## 1. How do you calculate the angle between two charges repelling each other?

To find the angle between two charges repelling each other, you can use the trigonometric function tangent (tan). The formula is tan(theta) = opposite/adjacent, where theta is the angle, opposite is the distance between the two charges, and adjacent is the radius of the circle formed by the charges.

## 2. Can the angle between two charges repelling each other ever be negative?

No, the angle between two charges repelling each other cannot be negative. Since the charges are repelling each other, they will always be on opposite sides of the circle formed by their repulsive force, resulting in a positive angle.

## 3. Is the angle between two charges repelling each other affected by the magnitude of the charges?

Yes, the angle between two charges repelling each other is affected by the magnitude of the charges. The stronger the charges, the larger the angle will be between them.

## 4. How does the distance between two charges affect the angle between them?

The distance between two charges has a direct impact on the angle between them. As the distance increases, the angle decreases, and vice versa. This is because the repulsive force between the charges decreases as the distance increases, resulting in a smaller angle.

## 5. Can the angle between two charges repelling each other change over time?

Yes, the angle between two charges repelling each other can change over time. This is because the forces between the charges can change due to external factors such as the movement of other charges or changes in the charges' positions or magnitudes.

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