Physics, asked by Prarthana5454, 10 months ago

Two small spheres 18 cm apart have
equal negative charges and repel each
other with the force of 6x10-8 N. Find the
total charge on both spheres.
[Ans: q = 2.93x10-7C]​

Answers

Answered by Anonymous
10

❏ Using ForMuLaS:-

If two charges \bf q_1 \:and\: q_2 are separated by a distance d, then;

The Force of attraction or repulsion between two charges is , given by the coulomb's Law.

\sf\longrightarrow \boxed{\large{F=\frac{q_1\times q_2}{4\pi \varepsilon_o d{}^{2}}}}

Question:-

Q)

Two small spheres 18 cm apart haveequal negative charges and repel eachother with the force of 6x10-8 N. Find thetotal charge on both spheres.

❏ Solution:-

Let, the two charges are \bf q_A \:and\: q_B and separated by a distance d.

GiVeN:-

\bf q_A \:and\: q_B = -q (let)

d=18 cm=0.18 m

Force=6\times 10{}^{-8}\:N

To Find:-

\bf q_A=? \:\: q_B=?

Now, Using the above coulomb's Formula.

\sf\longrightarrow F=\frac{q_A\times q_B}{4\pi \varepsilon_o d{}^{2}}

\sf\longrightarrow F=\frac{q_A\times q_B}{ d{}^{2}}\times \frac{1}{4\pi \varepsilon_o }

[Now,  \frac{1}{4\pi \varepsilon_o }=9\times{10}^{9}\:\:N.m{}^{2}.C{}^{-2}

\sf\longrightarrow 6\times 10{}^{-8}=\frac{(-q)\times (-q)}{{0.18}^{2}}\times(9\times{10}^{9})

\sf\longrightarrow\frac{ 6\times 10{}^{-8}}{9\times{10}^{9}}=\frac{q{}^{2}}{0.18\times0.18}

\sf\longrightarrow\frac{ 6\times 10{}^{-8}}{9\times{10}^{9}}\times0.18\times0.18=q{}^{2}

\sf\longrightarrow\frac{ 6\times 10{}^{-8}}{\cancel9\times{10}^{9}}\times\frac{\cancel{18}}{100}\times\frac{18}{100}=q{}^{2}

\sf\longrightarrow\frac{ 6\times2\times18\times 10{}^{-8}}{{10}^{9}\times10{}^{2}\times10{}^{2}}=q{}^{2}

\sf\longrightarrow\frac{ 216\times 10{}^{-8}}{{10}^{9+2+2}}=q{}^{2}

\sf\longrightarrow\frac{ 216\times 10{}^{-8}}{{10}^{13}}=q{}^{2}

\sf\longrightarrow 216\times 10{}^{-8-13}=q{}^{2}

\sf\longrightarrow\sqrt{ 216\times 10{}^{-21}}=q

\sf\longrightarrow\boxed{\bf q=4.65\times10{}^{-10}\:C}\:\:(approx)

\sf\longrightarrow\boxed{\bf q=0.465\:nC}\:\:(approx)

[ \because 1nC=10{}^{-9}\:C ]

Charge of Each Sphere = -4.65× \sf10{}^{-10} C.

Total Charge on both Spheres

= 2×(-4.65× \sf10{}^{-10} )C.

= -9.3×\sf10{}^{-10} C.

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