Given two metal balls (that are identical) with charges LaTeX: q_1q 1and LaTeX: q_2q 2. We find a repulsive force one exerts on the other to be LaTeX: 1.35\times10^{-4}N1.35 × 10 − 4 N when they are 20 cm apart. Accidentally, one the the experimenters causes the balls to collide and then repositions them 20 cm apart . Now the repulsive force is found to be LaTeX: 1.406\times10^{-4}N1.406 × 10 − 4 N. What are the initial charges on the two metal balls?

Answers

Answer 1

Answer:

[tex]q_1=\pm0.03 \mu C[/tex] and [tex]q_2=\pm0.02 \mu C.[/tex]

Explanation:

According to Coulomb's law, the magnitude of  force between two point object having change [tex]q_1[/tex] and [tex]q_2[/tex] and by a dicstanced is

[tex]F_c=\frac{1}{4\pi\spsilon_0}\frac{q_1q_2}{d^2}-\;\cdots(i)[/tex]

Where, [tex]\epsilon_0[/tex] is the permitivity of free space and

[tex]\frac{1}{4\pi\spsilon_0}=9\times10^9[/tex] in SI unit.

Before  dcollision:

Charges on both the sphere are [tex]q_1[/tex] and [tex]q_2[/tex], d=20cm=0.2m, and [tex]F_c=1.35\times10^{-4}[/tex] N

So, from equation (i)

[tex]1.35\times10^{-4}=9\times10^9\frac{q_1q_2}{(0.2)^2}[/tex]

[tex]\Rightarrow q_1q_2=6\times10^{-16}\;\cdots(ii)[/tex]

After dcollision: Each ephere have same charge, as at the time of collision there was contach and due to this charge get redistributed which made the charge density equal for both the sphere t. So, both have equal amount of charhe as both are identical.

Charges on both the sphere are mean of total charge, i.e

[tex]\frac{q_1+q_2}{2}[/tex]

d=20cm=0.2m, and [tex]F_c=1.406\times10^{-4}[/tex] N

So, from equation (i)

[tex]1.406\times10^{-4}=9\times10^9\frac{\left(\frac{q_1+q_2}{2}\right)^2}{(0.2)^2}[/tex]

[tex]\Rightarrow (q_1+q_2)^2=2.50\times10^{-15}[/tex]

[tex]\Rightarrow q_1+q_2=\pm5\times 10^{-8}[/tex]

As given that the force is repulsive, so both the sphere have the same nature of charge, either positive or negative, so, here take the magnitude of the charge.

[tex]\Rightarrow q_1+q_2=5\times 10^{-8}\;\cdots(iii)[/tex]

[tex]\Rightarrow q_1=5\times 10^{-8}-q_2[/tex]

The equation (ii) become:

[tex](5\times 10^{-8}-q_2)q_2=6\times10^{-16}[/tex]

[tex]\Rightarrow -(q_2)^2+5\times 10^{-8}q_2-6\times10^{-16}=0[/tex]

[tex]\Rightarrow q_2=3\times10^{-8}, 2\times10^{-8}[/tex]

From equation (iii)

[tex]q_1=2\times10^{-8}, 3\times10^{-8}[/tex]

So, the magnitude of initial charges on both the sphere are [tex]3\times10^{-8}[/tex] Coulombs[tex]=0.03 \mu C[/tex] and [tex]2\times10^{-8}[/tex] Colombs or [tex]0.02 \mu C[/tex].

Considerion the nature of charges too,

[tex]q_1=\pm0.03 \mu C[/tex] and [tex]q_2=\pm0.02 \mu C.[/tex]


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Answers

Answer:

D a conclusion

Explanation:

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Formation of Convection Currents

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Answer:

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A 350 kg motorcycle moves with a velocity of 30 m/s. What is its kinetic energy?
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Answer:

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A car is moving at 18 m/s when it accelerates at 8 m/s2 for 2 sec. What is his new velocity ?

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Answer:

Most electric charge is carried by the electrons and protons within an atom. Conversely, two protons repel each other, as do two electrons. Advertisement. Protons and electrons create electric fields, which exert a force called the Coulomb force, which radiates outward in all directions.

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Answers

Explanation:

Given that,

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The density of ethanol is 0.8 g/cm³

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Answers

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Anwer:

Key Equations

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Answer:

Properties of a photon would be:

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Answers

25 km/h hope this helps

Answer:

The answer is 20 km/hr

Explanation:

The average speed of an object given the time and distance covered can be found by using the formula

[tex]a = \frac{d}{t} \\ [/tex]

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From the question

d = 100 km

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[tex]a = \frac{100}{5} \\ [/tex]

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Answers

.20 m/s is the answer

Answer:

.20 m/s

Explanation:

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The answer is trueI just Finnishd

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Answers

Answer:

3

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Answers

Divide the distance traveled (0.30 km) by the travel time (0.50 hrs) and get the speed in km/hr. The direction is due west. 60 km/hr west

The average velocity of a car that travels 30 kilometers due west in 0.50 hour - 60 km/hour west.

Average velocity is the displacement of an object with the time change. To find the average speed of an object we divide the distance travelled by the time elapsed.

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average velocity = 30/0.5

= 300/5

= 60

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