Question

Two equal unlike charges, placed 3 cm. Apart in air. attract each other with a force of 40 N. The magnitude of each charge in micro coulombs is, take $\frac{1}{4\pi {\epsilon }_0}=9\times {10}^{9}SI$ units:

• A. 0.2
• B. 2
• C. 20
• D. 200

Answer 1

Answer: (B)

Force of attraction between two point charges $q_1$ and $q_2$ at separation r is given by $F=\frac{1}{4\pi {\epsilon }_0}\times \frac{q_1{q}_2}{r^2}$ (Here: $r=3cm=3\times {10}^{-2}m,$ $F=40N,\frac{1}{4\pi {\epsilon }_0}=9\times {10}^9$ ) $40=\frac{9\times {10}^9\times q\times q}{9\times {10}^{-4}}$ $q^2=\frac{9\times 40\times {10}^{-4}}{9\times {10}^9}$ $q^2=40\times {40}^{-13}=4\times {10}^{-12}$ = $q=2\times {10}^{-6}=2\mu C$