Question

Electrostatics.. numericals
1)two positive charges distant 0.1 m apart , repel each other with a force of 18 N. If the sum of the two charges be 9 micro-coulomb then calculate their separate values

Answer 1

The Coulomb's law of force between two electrically charged particles :
         q₁ , q₂ = electric charges on the two particles.
           r = distance between two particles = 0.1 m
      the particles are assumed to be point sized.
         Force F = 18 N 

        q₁ + q₂ = 9 μ C    --- (1)

$Force\ F=\frac{1}{4\pi \epsilon_0}\ \frac{q_1\ q_2}{r^2}\\\\q_1\ q_2=\frac{18*0.1^2}{9*10^9}=20*10^{-12} C,\ \ \ \ --\ (2)$

  Solve the two equations to get the values of charges.
     q₁ (9 - q₁) = 20
     q₁² - 9 q₁ + 20 = 0
       (q₁ - 5) (q₁ - 4) = 0

       q₁ = 5 μ C  or  4 μ C
       q₂  = 4 μ C  or  5 μ C

Answer 2

Gɪᴠᴇɴ

$\tt \longrightarrow{}Sum \: of \: two \: charges = 9 \: \mu c \\ \\ \tt \longrightarrow{}Force(F) = 18 \: N \\ \\ \tt \longrightarrow{}implies distance \: between \: them(r) = 0.1 \: m$

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ᴛᴏ ꜰɪɴᴅ

$\tt \mapsto value \: of \: q_{2}$

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Sᴛᴇᴘꜱ

$\bold{As \: we \: know \: that} \\ \tt \dashrightarrow q_{1} + q_{2} = 9 \: \mu c \\ \\ \tt \dashrightarrow q_{1} + q_{2} = 9 \times {10}^{ - 6} \: c \\ \\ \bold{As \: per \: Coulomb's \: law} \\ \tt\dashrightarrow |F|= \frac{1}{4\pi \epsilon _{o} } \frac{ q_{1} q_{2} }{ {r}^{2} } \\ \\ \tt \dashrightarrow 18 = 9 \times {10}^{9} \times \frac{ q_{1} q_{2} }{ {0.1}^{2} } \\ \\ \tt \dashrightarrow 18 = 9 \times {10}^{11} \times q_{1} q_{2} \\ \\ \tt\dashrightarrow q_{1} q_{2} = 20 \times {10}^{ - 12} \: {c} - - - - - (2) \\ \\ \bold{As \: we \: know \: that} \\ \tt \dashrightarrow q_{1} - q_{2} = { (q_{1} + q_{2}})^{2} - 4 q_{1} q_{2} \\ \\ \tt \dashrightarrow q_{1} - q_{2} = {(9 \times 10^{ - 6}) }^{2} - 4 \times 20 \times {10}^{ - 12} \\ \\ \tt \dashrightarrow q_{1} - q_{2} =81 \times 10^{ - 12} - 80 \times 10^{ - 12} \\ \\ \tt \dashrightarrow q_{1} - q_{2} = 1 \times 10 ^{ - 12} - - - - - (3) \\ \\ \text{From \: (1) \: and \: (3)} \\ \\ \green{ \tt\leadsto q_{1} = 5 \: \mu c} \\ \\ \green{ \tt \leadsto q_{2} = 4 \: \mu c}$

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