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Juliette [100K]
3 years ago
8

Two particles are 15 meters apart. Particle A has a charge of 6.0 • 10-4 C, and particle B has a charge of 5.0 • 10-4 C. The res

ulting Coulomb force is 12 N. At the same distance, what combination of charges would yield the same Coulomb force?
Physics
1 answer:
deff fn [24]3 years ago
7 0

Answer:

The combinations are

1. 2\times 10^{-4} C , 15\times 10^{-4}

2. 3\times 10^{-4} C , 10\times 10^{-4}

Explanation:

The force between two charges q and Q is given by Coulomb's law.

The coulomb force is given by

F = \frac{1}{4\prod \varepsilon _{0}}\times \frac{Q\times q}{r^{2}}

Where, r be the distance between two charges

According to the question,

r = 15 cm, Q = 6\times 10^{-4} C, q = 5\times 10^{-4} C , F = 12 N

Force remains same, distance remains same

so the product of Q and q be same

The product of Q and q is 30\times 10^{-8}

So other combination of charges are

1. 2\times 10^{-4} C , 15\times 10^{-4}

2. 3\times 10^{-4} C , 10\times 10^{-4}

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Where v= velocity

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4π^2/GMe = 4π^2 / [(6.67x10^-11 x6.0x10^24)]

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Therefore,

T^2 = (0.9865 × 10^-13) × r^3

r^3 = 1/(0.9865 × 10^-13) ×T^2

r^3 = (1.014 x 10^13) × T^2

To find r1 and r2

T1 = 120min = 120*60 = 7200s

T2 = 180min = 180*60= 10800s

Therefore,

r1 = [(1.014 x 10^13)7200^2]^(1/3) = 8.07 x 10^6 m

r2 = [(1.014 x 10^13)10800^2]^(1/3) = 10.57 x 10^6 m

Required Mechanical energy

= - GMem/2 [1/r2 - 1/r1]

= (6.67 x 10^-11 x 6.0 x 10^24 * 50)/2 * [(1/8.07 × 10^-6 )- (1/10.57 × 10^-6)]

= (2001 x 10^7)/2 * (0.1239 - 0.0945)

= (1000.5 × 10^7) × 0.0294

= 29.4147 × 10^7 J

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B

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