Two point charges +6 {C} and +10 {C} kept at certain distance repel each other with a force of 30 {N}. If each charge is given an additional charge of -8 {C}, the two charges [AP EAPCET 18 May 2024 Shift 1]

Correct Answer is : Attract with a force of 2N2 {N}2N

Correct Answer is : Attract with a force of 2N2 {N}2N

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Electrostatics

Section: Physics

Question : 31 of 32

Marks: +1, -0

Two point charges

+6 \mu \mathrm{C}

+10 \mu \mathrm{C}

30 \mathrm{N}

-8 \mu \mathrm{C}

Solution:

Given:

Initial charges:

\;q_1=+6 \mu \mathrm{C}=6 \times 10^{-6} \mathrm{C}

\;q_2=+10 \mu \mathrm{C}=10 \times 10^{-6} \mathrm{C}

Force of repulsion:

F=30 \mathrm{N}

Using Coulomb's Law:

F=\frac{1}{4\pi\varepsilon_0} \cdot \frac{q_1 q_2}{r^2}

Solve for

r^2

\;r^2=\frac{9 \times 10^9 \times 6 \times 10 \times 10^{-12}}{30}

\;r^2=18 \times 10^{-3}

Adding Additional Charges:

Each charge receives an additional

-8 \mu \mathrm{C}

\;q_1^{'}=+6-8=-2 \mu \mathrm{C}

\;q_2^{'}=+10-8=+2 \mu \mathrm{C}

Recalculate the Force Using Coulomb's Law:

F^{'}=\frac{1}{4\pi\varepsilon_0} \cdot \frac{q_1^{'} \cdot q_2^{'}}{r^2}

Substitute

q_1^{'}

and

q_2^{'}

F^{'}=\frac{9 \times 10^9 \times 2 \times 2 \times 10^{-12}}{18 \times 10^{-3}}

(From Equation 1)

F^{'}=2 \mathrm{N}

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