# Three 3.0 g balls are tied to 80-cm-long threads and hung from a single fixed point. Each of the balls is given the same charge q. At equilibrium, the three balls form an equilateral triangle in a horizontal plane with 20 cm sides. What is q?

q = 0.105uC

Step-by-step explanation:

We can determine the force on one ball by assuming two balls are stationary, finding the E field at the lower right vertex and calculate q from that.

Considering the horizontal and vertical components.

First find the directions of the fields at the lower right vertex. From the lower left vertex the field will be at 0° and from the top vertex, the field will be at -60° or 300° because + charge fields point radially outward in all directions. The distances from both charges are the same since this is an equilateral triangle. The fields have the same magnitude:

E=kq/r²

Where r = 20cm

= 20/100

= 0.2m

K = 9.0×10^9

9.0×10^9 × q /0.2²

9.0×10^9/0.04

2.25×10^11 q

These are vector fields of course

Sum the horizontal components

Ecos0 + Ecos300 = E+0.5E

= 1.5E

Sum the vertical components

Esin0 + Esin300 = -E√3/2

Resultant = √3E at -30° or 330°

So the force on q at the lower right corner is q√3×E

The balls have two forces, horizontal = √3×E×q

and vertical = mg, therefore if θ is the angle the string makes with the vertical tanθ = q√3E/mg

mg×tanθ = q√3E.

..1

Then θ will be...

Since the hypotenuse = 80cm

80cm/100

= 0.8m

The distance from the centroid to the lower right vertex is 0.1/cos30 =

0.1/0.866

= 0.1155m

Hence,

0.8×sinθ = 0.1155

Sinθ = 0.1155/0.8

Sin θ = 0.144375

θ = arch sin 0.144375

θ = 8.3°

From equation 1

mg×tanθ = q√3E

g = 9.8m/s^2

m = 3.0g = 0.003kg

0.003×9.8×tan(8.3)

0.00428 = q√3E

0.00428 = q×1.7320×E

Where E=kq/r²

Where r = 0.2m

0.0428 = kq^2/r² × 1.7320

K = 9.0×10^9

0.0428/1.7320 = 9.0×10^9 × q² / 0.2²

0.02471×0.04 = 9.0×10^9 × q²

0.0009884 = 9.0×10^9 × q²

0.0009884/9.0×10^9 = q²

q² = 109822.223

q = √109822.223

q = 0.105uC

## Related Questions

-8x-x=x-4x plz do it step by step ans show me

Answer: 3x - x = 0

Step-by-step explanation:

1.Simplify -8x - x to -9x.

2. Simplify x - 4x to -3x.

3. Divide both sides by -3.

4. Subtract x from both sides.

5. Simplify 3x - x to 2 x.

6. Divide both sides by 2.

there are four pizzas which each have 12 slices. these pizzas will be divided between 15 people. how many slices does each person get if they are split evenly

3.2 so they would each get around 3 slices!

3.2

Step-by-step explanation:

so 3 slices for each

Use a Venn diagram to answer the question. A survey of 180 families showed that 67 had a​ dog; 52 had a​ cat; 22 had a dog and a​ cat; 70 had neither a cat nor a​ dog, and in addition did not have a​ parakeet; 4 had a​ cat, a​ dog, and a parakeet. How many had a parakeet​ only?

There are 13 families had a parakeet only

Step-by-step explanation:

* Lets explain the problem

- There are 180 families

- 67 families had a dog

- 52 families had a cat

- 22 families had a dog and a cat

- 70 had neither a cat nor a​ dog, and in addition did not have a​

parakeet

- 4 had a​ cat, a​ dog, and a parakeet (4 is a part of 22 and 22 is a part

of 67 and 520

* We will explain the Venn-diagram

- A rectangle represent the total of the families

- Three intersected circles:

C represented the cat

D represented the dog

P represented the parakeet

- The common part of the three circle had 4 families

- The common part between the circle of the cat and the circle of the

dog only had 22 - 4 = 18 families

- The common part between the circle of the dog and the circle of the

- The common part between the circle of the cat and the circle of the

- The non-intersected part of the circle of the dog had 67 - 22 - a =

45 - a families

- The non-intersected part of the circle of the cat had 52 - 22 - b =

30 - b families

- The non-intersected part of the circle of the parakeet had c families

- The part out side the circles and inside the triangle has 70 families

- Look to the attached graph for more under stand

∵ The total of the families is 180

∴ The sum of all steps above is 180

∴ 45 - a + 18 + 4 + 30 - b + b + c + a + 70 = 180 ⇒ simplify

- (-a) will cancel (a) and (-b) will cancel (b)

∴ (45 + 18 + 4 + 30 + 70) + (-a + a) + (-b + b) + c = 180

∴ 167 + c = 180 ⇒ subtract 167 from both sides

∴ c = 180 - 167 = 13 families

* There are 13 families had a parakeet only

Math Is TU parallel to VW explain

Answer: C ( yes, both lines have a slope of 2/3. )

Step-by-step explanation:

Step-by-step explanation:

In this equation what do i have to change to make x equal 0 instead of 1/4
2√x+4-2=3

To solve for x:
- add 2 to both sides
2/x+4=5
- subtract 4 from both sides
2/x=1
- divide both sides by 2
/x= 1/2
- square both sides
x = 1/4

What are the zeros of the function below? Check all that apply